... My Step-Dad is very good at this and he has Durst that he converted to a "cold light head???" and says I definitely want one with a "cold light head". Is this really important?
Be careful - people always advise others that they should buy something just like the one they have: it is often the only thing they know; it validates their choice - and why wouldn't they have made the best choice?; and if it turns out to have been a lousy choice - well, misery loves company.
Good advice usually takes the form: "I had an A, I replaced it with a B, didn't really like the B so now I have a C. But I think a B might be the best choice for you." [Assuming, of course, they aren't just trying to sell you their old B.]
Cold light heads are an acquired taste: some swear by them, some swear at them. They are probably not the best choice for someone just starting out. A 'diffusion head' enlarger will bring the supposed benefits of a cold-light head without the headaches. Identical prints can be made with condenser enlargers, diffusion enlargers and cold light enlargers - though each will need a slightly different grade of paper to produce matching prints. Identical prints can also be made by adjusting the negative development and using a single grade of paper.
There are a lot of used enlargers on the market. Some choices are:
Durst made some very nice compact enlargers that would enlarge up to 6x6cm negatives. The problem with Dursts is they often require odd accessories like LAPLAs and WTFIIs that can set you back the price of the enlarger. Make sure it comes with all the bits you will need: lens boards/adapters, negative carriers and condensers. If you need an enlarger you can put in a drawer at the end of the day these are likely your best bet.
Saunders/LPL enlargers are also very nice. They are diffusion models - so instead of the condenser sets you will need the complete set of 'light chambers'.
Beseler 23's are very common. They are cruder than Dursts or LPLs but they also have a certain cockroach toughness to them - you can't kill them. You can not put them away when not in use [or not easily].
Omega made the very nicely made 'B' series back in the 60's. Though long in the tooth, if in good condition, they work well and accessories are easy to find on ebay. Omega made a newer family of MF enlargers in rather a bewildering array of models: some are condenser, some diffusion.
Meopta enlargers are another good choice, again make sure it comes with all it's bits.
You will want to start out using variable contrast RC paper. Graded paper no longer comes in a wide variety of grades and so you need to be very good with your exposure and developing technique and produce nearly perfect negatives. VC paper can usually pull a reasonable print from a train-wreck of a negative. RC paper processes faster with less fiddling - a good choice as it lets you see the finished product quickly so you get feedback on your work while you may still remember what it was you did when making the print.
VC heads let you dial in the paper contrast when using VC paper. However, the same results can be had with VC filters than either go in the head or under the lens. It is also possible to use a color head for VC paper, but you often can't get the full range of contrasts.