my thought was when fermented just fill the keg make it airtight and store and let naturally carbonation happen
Yep I see where you're coming from, but in order to get the desired level of carbonation that way you'd have to (1) transfer to the keg before fermentation is finished; or (2) add priming sugar once it's in there. I'm not a big fan of either option: (1) requires careful judgement, and (2) involves waiting for secondary fermentation to complete before you can start the
'quality assurance testing process'
then maybe a few weeks before use start adding some Co2 from cartridges
If you mean those little mini 'sparklet' cartridges, they work but are a
bit of a pain in the backside because you will go through them like there is no tomorrow.
You really need a gas pressure regulator anyhow, so that you can serve the beer without just delivering pints of foam; so unless your budget is extraordinarily tight you'd be better off getting either a SodaStream bottle (available from Robert Days, Argos store-in-stores at large Sainsburys etc) or a pub-type cylinder (not difficult to get, and much cheaper in the medium term).
Generally the process works like this:
1) when fermentation is complete i.e. about 5 days after the SG has stopped falling, flush the keg (Corny, King Keg, whatever) with CO2 to expel the air - then transfer the brew.
2) seal the keg, connect the gas and set the regulator to about 20psi depending on the style of beer
3) leave for 2-3 days or if you're in a hurry lie it flat and gently 'rock' for 10 mins or until the regulator stops feeding in gas
4) leave for 2-3 days to settle (unless you're impatient) then reduce the regulator to serving pressure 3-6psi, and start sampling
5) if the carbonation is too high or low then add more gas or vent off.
of course the beer will continue to improve in appearance and quality if left to condition - but there's no reason not to get a few pints down while that's underway :-)