for the lack of info I will just lay out my system, you can figure out how to mod it for your needs
8* 6V golf cart batteries series perallel. (I started off with just 2 and they held my 14 footers load fine, a fridge, lights, a tv and 12v dvd player) they all feed into a colector box with 8awg cut to the mm in same lengths
200Amp fuse > 2AWG 2feet > Inverter 1800w w/transfer switch
from the colector box 0/1 guage to solar charger and load hub, solar charger is 2awg, load is fed with 6 guage both legnths are 5 feet
Solar charger is a Tristar Mppt 60 connected to a 540w array (Powers great in summer but due to furnace not quite enough during winter)
Now those batteries power a 30 foot trailer for 6 days with lights (Flourescent and led) my computer, furnace, microwave, coffee pot and more.
The generator is 50 feet away remote start via 10awg and conects to the inverter via twist lock, the battery charger is 40Amps, if the batteries are low it takes a full day to charge with the genset.
For you, 2 high quality golf cart batteries, idealy 4 or get rid of the microwave or coffe pot, I recomend ditching the coffee pot and do it the old fassioned way, boil water in kettle then pour over the goffe grounds in a filter, worked better imo.
Inverter you want good 2 guage wire short as possible, forget about 6Amps barely keep up with the battery, they're garbage! you need nothing smaller then 20Amps
the genset feeding A/C 14 to 10guage will be fine, given your budget and energy draw I'd say 12 guage will be plenty good enough
In short 2*6v golfcart batteries (4 ideal),
20Amp or better charger (40Amp recomended)
50foot 12 or 10AWG extension cord
good french press or stove top kettle and a nice filter basket for making coffee
Go to Superbright LEDs.com or ebay and get LED bulbs for the fixtures, or get the puck lights!
And some fuses 200amp slow blow for the inverter, (Conect a 300A between the batteries) and then a fuse pannel with the standerd 15A circuits (Burning to death really wrecks the rest of your life!)
toss the little batteries and the light packs keep the fixtures.
And either get a Bogart trimetric for an RV will cost ya aqbout 200 or less or a very good expanded volt meter (Volt meter the least usefull but better then nothing) as this will allow you to run the genset when only needed and allow you to use power in a wiser fassion
Now to the solar! a single 250W pannel is small enough to handle along, hard but able to, so you can go with two 130w pannels to make it easier, this will allow you to run with virtualy never needing the gen set, at Sunlec you can get stick on 130w pannels for under 200 dollars! but run for a bit with just the gen set and batteris till you figure out what you need.
the whole thing when assembled properly will barely take up any more room then the current set up, infact if you took a day possioning it all it would be smaller!