A regulator is sexy. I'd want to buy that first, too! It's tough to pay for a wetsuit first if you don't know what you'll be wanting to do. Warm water? California cold water? REALLY cold water? I'd say, give in to the urge and get a regulator! They're fun to play with in the living room.
I'm going to take a flyer here and get flamed. But here goes. Since the OP said "best-cheapest", then hands down there's a great solution:
Go on EBay and bid on the prettiest Scubapro Mk10 and G250 you can find (not G250HP). I'll bet you can get a great set for under $150. THENNNNN...take them down to your local dive shop and ask them to service them. No matter what some EBayer dumped on you, a good dive shop can replace diaphragm, poppet, orifice, what have you for not much more money. $30 for each reg plus parts is my LDS' charge. You'll have a great regulator that will last another 20 years for less than $250. Parts are everywhere. And the Mk10/G250 combo beats a lot of other sets hands down.
Yeah, you can spend more. Yeah, you can buy new. But Mk10/G250 is sexy. Just choose a set with no scratches. Or buy a new G250 face plate from Annie on EBay for $20.
The hard part is worrying that you'll get a piece of junk. But even there you're OK. If your Mk10 has "IP creep" (ask your dive shop what that means), you have 14 days to send it back to the seller as "Not as described".
Then take the leftover money your parents were going to spend on you and you're halfway to your next toy.