I've only just come back to this forum after a rather long break due to illness, and this is one of the first posts that caught my eye. I had intended to provide a lot of technical help to these forums last year, relating to off-grid services of all types in order to help out those folk whose knowledge and skills are more focussed on agriculture than things technical.
At some point I'll be producing a manual which will cover every aspect of power generation, fuels, pumps, water extraction and supply, sewage, heat sources etc, which will be offered at low cost to F2F book owners. A lot of this information is already being put to use on my own 14 acres which will now finally get the attention it deserves after such a long break.
Meanwhile, just to add my tuppence worth to this thread, I assume that your inverter is a fairly low wattage square-wave type? Hence not being able to run a TV, and you'll probably find that anything with a motor will run poorly too. Without getting too technical, a square-wave (or modified-wave) inverter is a crude (hence cheaper) way of producing the 60 hertz frequency needed for AC power. The current spends too long at 0 volts whilst cycling up and down 60 times per second, and hence can't properly run motors, including those in fridges, due to their need for a smooth supply. TVs are also affected by this. The analogy would be that of pedalling a bicycle - you wouldn't get far if you kept pausing every time the pedal reached the top of it's stroke!
The solution is to use a 'pure sine-wave' inverter which replicates mains electricity far more efficiently. It costs a bit more, as a quick glance at Ebay will show, but will run everything within it's rated capacity. I personally run a 3kw inverter which will even handle my dishwasher (bit decadent I know!), and I use a smaller 1kw inverter for general standby duty. The bigger one is only turned on when needed due to it's higher 'idle' power consumption. All inverters consume power whilst turned on, even if not in use, and the larger cheap ones can eat 1 amp or more per hour on standby. A high quality pure sine-wave unit can have a standby rating as low as 0.2 amp. It should also be noted that induction motors (i.e. power tools, fridges, pumps etc) have a startup surge of upto 10X the rated current. In other words, a fridge rated at 90 watts will require 900 watts to start up, hence my use of the 1kw inverter to keep my fridge running. My advice: buy the best quality second-hand pure sine-wave inverter that you can afford for the size you need. There are loads on Ebay all the time but avoid the Chinese-made ones like the plague!
Second point, more briefly, if you're going to get a diesel generator then try to get an older model with an in-line injector pump, as opposed to the modern rotary injector pump. The good reason being that the in-line models are lubricated by the engine oil but the rotaries rely on lubricant in the fuel onl;y. This becomes a serious issue when using home-made fuels, including a lot of bio-fuels, which don't have lubricants in them. Injector pumps are incredibly reliable until abused, after which they become incredibly expensive to repair (definately not a DIY job!). I mention this because I intend growing a couple of acres of rapeseed oil to power my generator (almost) for free. I'm sure most of you know that vegetable oils make a good fuel for diesel engines, and rapeseed oill is a particularly good fuel in this respect. An acre will produce at least 2000 litres of cold-pressed oil, with the remaining two thirds of crop weight making either an excellent high protein animal feed or very efficient fire fuel.
Sorry if I've rambled a bit, there's a huge amount of information on off-grid services. I'll try and get it across in a structured fashion in future.