seay00, I've been trying to nail down the best team to leave you with. Your '59 Giants give you a handful of solid starting pitchers but not much in the name of a bullpen. They also have Cepeda and Mays to spark the offense, plus a partial McCovey season I'm sure you'd love to be able to use. The '49 Browns are nothing to write home about, giving you precious little to add to your pitching staff (and no cheap arms at all). A couple of usable catchers and outfielders and a decent 3B in Dillinger though he can't field much. Only one hitter is under $1M, too. So you don't have much flexibility with them.
Any team I can give you now has at least somewhere that helps you a little. I've looked at 5 really good candidates trying to see where I can make this as awkward as possible. I've finally settled on the 1949 Philadelphia A's.
The A's only have 20 eligible players, just 7 of them pitchers. But aside from a very walk-prone Bobby Shantz you won't want to use any of the other ones either. And if you do, none of them are cheap. If you also don't want to use lousy Browns pitchers, you start to run out of position player slots pretty quickly.
The A's do give you some decent options, though they're all a tad on the pricey side. SS Joost is good, but can you afford his $7M salary? They have a couple usable OF who could play CF if you don't use Mays ... but let's be serious, you want to use Mays. And do you want to overpay for guys with 700+ PA who are basically average hitters to put next to him? And if you do, which Browns do you take? Only so many OF spots, and two of the Browns' best hitters play out there, too, and are more affordable.
Did I mention that your Giants and Browns had no cheap backups at 1B or 2B? Well, don't worry because neither do these A's. I feel like you're gonna have to waste some money somewhere unless you can find a perfect match team in Round 4 that fills every gap. Best of luck!