Generator charge to battery question

I think you may be a little confused there Dave.
If your 12 volt nominal dc generator is capable of 1,000 watts output, then 1,000 divided by 12 = 83 amps but, chances are it may not actually be able to produce maximum output for very long a period of time because of increasing heat. I would have know its manufactures specifications to know for sure. As for wiring your inverter straight to the generator, consult its manufacturer. Chances are it would be okay as long as you have the correct wire size and fuse in line but, there could be sensitive electronics in the inverter that may not handle a lot of spikes and dips in voltage or the ripples formed by some generators may cause excessive heat on the electronic circuitry.
Consult its manufacturer.

At maximum output, your 2,500 watt inverter can produce 20 amps at 120 vac.
To do that it will be pulling 208 amps from a 12 vdc source.
2500 / 120 = 20
2500 / 12 = 208
If your generator produces a maximum of 83 amps then your inverter will only be capable of 996 watts.
12 X 83 = 996
996 / 120 = 8
On almost all electrical gadgets there is a label or tag that states the amount of power it needs to run. It will show either volts and watts or volts and amps. Either way you can get the third value from those two by multiplication or division. Look on your dishwasher, if its more than 8 amps or 996 watts at 120 vac, you cant use it.

Nix the idea of using a car cranking battery altogether. If your going to use a battery get true deep cycle batteries. I can tell you too that those so called marine "deep cycle" batteries are not true deep cycle batteries, the are just cranking batteries with a larger than normal reserve. A good battery for beginners would be two 6 volt 220 amp hour "golf cart" batteries wired in series for 12 volts nominal. For one thing you should be able to find them locally, and you wont have to pay for shipping. You will need some sort of battery monitor. 220 amp hours will power your inverter at the maximum output of 2500 watts for 1 hour BUT! The batteries will be completely dead. Not a good idea. You only want use 50% or less of its capacity before recharging them. I prefer keeping them in the top 20%.

Look at the power requirements of all the electric gadgets you want run. Determine how long a time you will use each over a 24 hour period and add it all up, then divide by 12 and multiply by at least 2. Example:
TV - 80 watts for 4 hours = 320 watthours
Computer - 70 watts for 2 hours = 140 watthours
Lighting - 100 watts for 6 hours = 600 watthours
Total = 1060 watthours
1060 / 12 X 2 = 177 amphours
Your generator would have to run at max. for about 2 hours to replace that.
177 / 83 = 2
Make sure you know the correct wire size for everything you wire up Dave otherwise your parade could end in fireworks, capisce?
Look up Ohm's Law for more about this math.