If he can stand over a 54cm with some clearance already, it would be a mistake to buy a 50cm or 52cm. Okay, maybe a 52cm if you can find a decent used one for dirt cheap, knowing that you will probably replace it pretty quickly.

It you not make any sense to buy him expensive new road bikes while he's growing and he may only ride them a year or two at most. Look for a decent 90s or better aluminum bike to get him started. You don't know if he will even keep riding, when in a couple of years he's going to get the itch to drive, and he may leave cycling for a while.

My oldest son turned 30 years old last year, and he surprised me be asking if I still had his old mountain bike, and if I had a road bike he could try riding. He had not ridden a bike since he was 15 years old. I still had his last mountain bike (adult sized, I stored all my kids last bikes in the garage hoping they would want them back some day). I suggested that he ride the mountain bike for a couple of months to get used to riding again, and if he still wanted to try a road bike (he has never ridden a road bike), then we could see about getting him a road bike.

He took his mountain bike to his house, and in less than two months, it got stolen when one of his room mates borrowed it to ride to work, because his car was not running. I went trolling Craigslist and found a 88 52cm Trek 1000 with Shimano 105 on it, 90 minutes away for $30 (I think I could have fit him on a 54cm, but the 52cm seems to fit him fine with a longer handlebar stem). From the looks of it, the bike was left outside in the sun for years (the Dupont Imron Trek painted it with still looks great) before I rescued it. The tires, tubes, and seat had rotted to shreds. The wheels were surprisingly true, I greased the wheel bearings, bottom bracket, pedals, and headset. Then replaced the tires, tubes, rimstrips, brake cables and housings, and the seat. I updated to dual pivot brake calipers, replaced one brake lever, and changed the handlebar stem and handlebars to fit the bike to him.

I don't think I have $125 in it yet, and I could not buy a similar used bike in same condition for less than $300-$400. If he rides the bike hard this year, we can see about finding him a newer bike with a more modern drivetrain (it has a 6-speed freewheel and downtube shifters), if we don't upgrade the 88 further. But it would be so easy to upgrade it. I checked, it will take a 130mm rear wheel, and I have spare freehub wheels and new Shimano FD2300 front and rear derailleurs (from eBay, they cost me $5 each), so I could upgrade him to a 7, 8, 9, 10 cassette pretty easily.

54cm framed bikes are hard to find as they are probably the most popular size. 56cm and 58cm bikes are usually what I find for sale. 50cm and 52cm bikes are a little easier to find, and in less demand, so the prices that you can get them for are actually a little lower. When dealing with Craigslist and eBay Sellers, don't expect them to be advertising the size of the bikes for sale accurately/correctly. I swear most bikes I go to look at are a different size than advertised, and even when I talk to Sellers before I drive over to look, and have them measure the bike frame, they get it wrong.

You should be able to find decent used bikes to go look at for less than $150 (I bought or traded for eight 1990s and 2000s Trek road and mountain bikes last year, and didn't pay more than $100 for any of them except a 2300 composite bike). Make sure that they are new enough to at least have 700C wheels. That sure ensure that the bike is new enough for you to be able to find replacement parts easily from local sources (and not have the bike down while you hunt for some part no-longer made by a defunct company on the Internet). If you are willing to spend $275-300, you should be able to find a 2000s Trek or Specialized road bike (for example, there are several 2002-2007 Trek road bikes selling for $300 or less in the SoCal area right now.

If you buy right, when you go to sell you won't lose any money.