The link I added shows that most flooded/wet/ sloshy 12v 'deep cycles' are not really deep cycle batteries. There are a few, the trojan t-1275 is, but the $ shows it.
It does have 150 amp hours of capacity where as most group 31 batteries, which is generally the largest car jar size battery available, top out at 130 amp hours, and in my opinion, having had one, this capacity rating is too generous. I'd say 110 to 115.
Anyway. Just be aware that a battery with a 'deep cycle' sticker might be little better than a starting battery in the deep cycling department.
Marine / deep cycle on left, GC-2 authentic deep cycle golf cart battery on right.
Charging USB devices is best done with a 12v to 5vDC usb port, rather than through an inverter.
Example. not a specific product/brand/seller recommendation:
An inverter has a standby load, meaning it draws energy turned on powering nothing, and when it is powering something it is only ~80 to 85% efficient.
Having a Huge inverter, powering a small load is much less efficient than a smaller inverter powering a smaller load, in general.
Lots of people get a huge inverter, but then do not have enough battery capacity to come anywhere near being able to provide that amount of load. its kind of like a drag car which needs 50 gallons of gas to make a 1/4 mile run, but having only a 10 gallon tank.
A laptop can also be powered by a DC to DC 'car adapter' which is more efficient than using the inverter to power the provided power brick. The issue with these is the ciggy plug itself cannot withstand passing more than 60 watts for a long time. I've been using the PWR+ brand of laptop adapter on my dell, for a decade. Only issue has the ciggy plug but it saves 9 to 15 watts of energy over using my inverter to power the originally provided AC/DC power brick. 32 watts vs closer to 50 watts through the inverter. that is significant savings, especially on a single battery. MOst laptops have 'car adapters' available. the universal ones can be OK, in some applications under 60 watts, but the 'universal' part of the connector can become problematic too.
I don't know what a 120Vac home receiver's wattage really is, but it would be nice to know that figure before recommending an inverter size.
Without that receiver/ amplifier, you could likely get away with a 150 watt inverter, but if you use a ciggy plug to power it, instead of leads right to the battery you run into that 60 watt issue again.
Pure sine wave inverters are more expensive than modified square wave inverters, but if powering the 120vac amplifier, a MSW inverter will likely have an intolerable 60 HZ buzz/ whine in the background.
The laptop power supply and the USB power supply will not have any issues with a MSW inverter.
Some power tool battery chargers WILL have issues with a MSW inverter.
The price difference between PSW and MSW inverters is much less than it was a few years back, but the higher quality names like Samlex and GoPower are still pretty pricey.
I had a 400 watt Wagan Elite PSW inverter, but it did not last very long. I loved its small physical size and it was when new able to exceed 400 watts of output and the fan only ramped up loudly at max load.
My 800 watt coleman MSW inverter bought in 2005 or so keeps on going, but its fan is always annoyingly loud and it draws 0.62 amps turned on powering nothing, which is more than my 12v dc compressor fridge consumes, 95% of the time.
On the back of the 120vAC receiver/amplifier you intend on powering, look for a power figure, something like 2.3 amps @ 115vac or it will just say wattage. volts times amps equals watts so in the above example 2.3x 115 is 265 watts. My pioneer BT head unit says 52 watts x 4, for 208 watts of load. I've never measured anything close to this, but my tools cannot measure the peaks during bass thumps. If I crank it upto uncomfortable volumes it is drawing about 9.5 to 10.5 amps. this is about 120 watts, depending on battery voltage.
Most phones draw a maximum of 2.1 watts at 5v. This is 10.2 watts. Lots of inverters come with USBoutputs, but the inverter needs to be turned on, and the standby load of the inverter on can be 6 watts, on top of the 10.2 watts the phone can draw through charging via the USB port.
My laptop requires a 90 watt power supply. It only can draw 90 watts from it when the laptop's battery is dead, and it is performing some task requiring more of its CPU, like streaming HD video or spinning a DVD. Typing this it averages about 33 watts of consumption.
Inverters should be wired close to the battery, but not located in the same compartment as the battery, in case charging gasses are present( think potential BOOM) and have been taking some sulfuric acid mist with them. ( corrosion) Use 120V extension cords to reach 120V appliances from inverter, rather than putting inverter at distant location from the battery. Using too thin and or too long of DC cables to teh inverter can have its low voltage alarm start screaming well before the battery is in danger of being overdepleted, and have it not come anywhere near its wattage output rating.
In general AGM batteries are much safer inside passenger compartment, and they also generally hold higher voltages under load, compared to their flooded marine brethern. The line between deep cycle and starting is blurred when it comes to AGM's but most of the AGMS sold in autoparts stores are manufactured as cheap as possible starting batteries, and will not do very well in deep cycle duty.
The Deka intimidator is widely relabelled and sold by Autoparts stores, and did very poorly in some deep cycling tests where they used it in partial state of charge cycling duty, as most people use deep cycle batteries, meaning the next discharge begins before teh battery had time to reach true full charge.
It proudly says deep cycle on it. East penn/Deka can make a very good battery, but the 'Intimidator' is not one of them. But it is competetively $$ and easily available.
AGMS are a bit more finicky in regularly requiring reaching a true full 100% charge to retain their capacity. their greater price does not make them immune to chronic undercharging, which is pretty danged widespread the world over as most people seem to think an alternator is a magical, physics defying, instant battery charger that makes free power.
Most people will never get any better life from an AGM in a starter battery role, for the ~60%+ greater price tag. The benefit would be lack of battery terminal corrosion/ charging gasses and if drawn very low, unintentionally or not, are likely to still have more Cranking amps available, than a flooded battery of same size group, to start the engine.
The lesser$$ AGMS do not have the super low self discharge of high$ AGMS. They are better than flooded batteries which can self discharge 1% per day it their half life and 15% per month when new. The high $$ AGMS self discharge 1 to 3% per month, at 77f., low $ agms can be as high as 7% when new and double that when old.
The higher the temperature the higher the self discharge.
The less healthy the battery the higher the self discharge.
Here is a pretty good battery life calculator. The Peukert effect basically says the larger the load on the battery, the less overall capacity it has to give. The default on the link below is a peukert number of 1.1. most manufacturers do not provide a peukert number, but odyssey AGM, a top $$ top dog super high CCA battery, claims 1.15 for their group 31. for a new flooded marine battery I'd use a 1.2 peukert number and expect it to climb towards 1.5 as the battery nears end of life/ useful capacity. http://www.csgnetwork.com/batterylifecalc.html
So as an example, say you get a single group 31 battery rated at 110 amp hours of capacity, and are powering a constant 120 watt stereo load, lets just call that 10 amps of load.
Under that load the 115Ah battery with a 1.2 peukert number can only provide 72.56 amps hours total. You could run the stereo for about 3.6 hours before the battery, assumed to be in top health and fully charged when the stereo was turned on, for 3.63 hours, hits 50% charged.
In general it is recommended to not take a lead acid battery, 'deep cycle' or not, below 50%. I do, but only when I can immediately apply a charging source for long enough to return to full charge.
Reaching true full charge from the 50% range, in less than 6.5 hours, is nearly impossible. It assumes a healthy battery and a high amperage charging source seeking mid to high 14 volts, and then holding them there the whole 6.5 hours. The more abused/old the battery the longer it takes. Eventually the capacity will decline to the point the battery can no longer be useful other than as a core charge on a new one. How long this takes depends on how well it is recharged as well as how much expected/ needed capacity the battery has left to give.
A lot of personal philosophy can come into play here, in terms of how often replacement is acceptable to the battery owner. I try to make them last as long as possible, but also work them hard. when worked hard I make sure they get what they want afterwards, and that is a prompt recharge to a true full state of charge.
A lot of people just replace as needed, using the warranty as much as allowed. Most marine batteries have shorter warranties and perhaps none at all.
I used to do this but always found I needed a new battery when it was the least possible convenient time to do so. I used to dread the process of trying to warranty a battery and decided to learn how to never need to use the warranty, by not overdischarging, and being able to reach true full charge regularly.