As has been said, one of the problems youll have is the paint your going to be able use at home, not so much the equipment ...
They have tightened up on the supply of most types of automotive paints to the man-in-the-street in the last few years.
The main paints...
Celulose - very hard to get these days from factors in specific tints, i order direct from manufacturer for my business, and they do not supply in less than 2.5l tins. Your also limited to less tinters than a few years ago, which means unless you are very good at mixing by eye you might run into colour match problems. Its also 2x as expensive as it was when he law changed 4 years ago and banned its general use... It also dries relatively matte, it dosent have that high-gloss 2-pack shine which most cars from the 80's onwards were painted in.
Its very easy to use & spray, but hard to get a nice, long lasting finish with. You think you have a nice finish, it drys back after a few weeks and can look 'orrible.... And its relatively brittle when its dry... Perfect on pre-80s cars though !
2-pack varients - up until recently, industry standard. You can still get the 'old' 2-pack in most mixes from old stock even now. The new 2-packs are high solids with a lower iso content. We use these, good tinter range, relatively easy to use, good straight from gun finish and lasts well. You dont have to be quite as anal with prep with these as you would with celly. I wouldnt reccomend it without an air-fed mask though. Its still nasty stuff.
Water-based - forget it for spraying at home. Really. Even then you'd still use a 2-pack primer and laquer....
1-pack Acrylics or Acrylic Enamels - most rattle cans are this now, and would be what you would be able to use at home. its somewhere in the middle of celly & 2-pack for ease of use & finish. Good range of tints, good availability. You get this from your local factors.
There are numerous other paint types & systems and developing all the time, but these are the one's youve heard about or would encounter most of the time. You might run into problems buying it though outside of rattle cans, unless you have a friend in the trade to help out there ?
Equipement wise, Griffs Devilbiss GTI is a good choice for touch-ups. We still use the GTI's predecessors - the MP & MPS as our main guns ( if anyone has either of these going spare, ill buy them off you.. ! ). Great for touch-ups. Ive spent 20+ years collecting different guns for different jobs & paint systems. Long term, quality counts.
Compressor, if your going to be doing basic car repair work as well, air tools are the best ! But you'll need a large reservoir otherwise it will be firing up every 15-20 seconds.... think 150 litres minimum. If you buy a 50 litre compressor, forget about using it for anything other than touching up paintwork, but that may be fine for your requirments
Air supply to gun has been well covered above, so no need for me to expand on it.
One important point to mention, is that most compressors over 100 litres require more power to run on than a household plug socket can supply. Last thing you want is to buy a nice high-cap compressor than you have to install a 32amp direct supply in your garage... and of course most quality high-capacity compressors are 3-phase, which would be more expense getting that wired in ! Check the power requirements before you buy anything...
Whatever you do, whatever you buy, the golden rule is that paintwork is all about prepwork ! Get that right, and you will have a good finish even with cheaper equipment.
Sorry for the long post, had time to kill on a long sunday night...