My usual method is to ferment and clear/mostly clear in the bucket, then transfer to keg. I use gas like you are saying which is quicker and a little more expensive, but you can prime with sugar, leave it in a warm place for a week and it'll be carbonated. You need about 80g of sugar if you're doing it this way, heat it into a little water so it's dissolved and add it when you keg. You won't need to add any gas if you choose to carbonate with sugar, except for maybe near the end.
You can only manage a low level of carbonation with a plastic keg, but it's enough for me so far so don't worry! Clearing in the bucket will mean less trub and sediment in the keg, meaning you tip it at the end to get the last few pints out. It's up to you when you take it out after fermenation has completed, that's just my preferred method. The cold will also help the clearing process, but it's only a time issue, no quality really involved. To bottle from the keg you'll want to get a simple attachment that lets you bottle with ease, they're available at most LHBS.
To know when it's done you really need a hydrometer, they're very inexpensive and will let you know the sugar content of your beer. Most beers will finish up around 1.010-1.015 - a little residual sweetness from unfermentable sugars - and start at 1.040-1.060 (or more for a high strength beer.)
You are likely to see your beer gradually start bubbling and there will be a thick layer of froth. As this slows and calms down, fermentation will come to an end. You can potentially have a beer ready in 2 weeks in decent conditions, but any questions just let us know and we will guide you in the right direction :)