personaly, if i were going to an inverter, i would opt for a pure sine wave output.
u should be able to pick one up for under $500 that has a cont output of 2Kw. if u do a little figuring, u may be able to do it on 1.5K or less. the coffee pot and microwave will definately be ur downfall.
ur lighting and cpap can be run on dc. u can probably pick up a cord at radio shack for ~$10 or from ur medical supply co for ~$75. Unless u work shift work, u could probably switch the inverter off at night. (consider the power drain while the inverter is on and in standby).
to save the energy for coffee making, consider visiting ur neighbor and having coffee with them.
the pure sine wave may not be necessary but electronic and motor driven items prefer it.
if u think abt it, tv, microwave, fan, coffee pot is abt all that requires AC; the other big users run of gas or DC.
word of mouth on what others are using is the best way but u can do an internet search for inverters and see what is out there and how much they are.
on the supply cable, mount as close as possible to the bat to minimize the supply cable.
also consider how ur going to tie it into the 120 supply. consider if u plug into the normal AC input, the converter is going to run and use power unnecessarily, u can unplug this or kill the breaker to it.