We've talked about the first round prospects for the Rays, so let's look at a few names for the other early rounds. Trying to sort out 3-5 names for pick 30 is pretty hard with all the variables beforehand, trying to do so for picks in the 70s is just ludicrous.
2nd Round
Mychael Givens, SS/P, HS (FL)
Some teams have him listed as a third rounder. That means if the Rays want him, they probably have to take him in the second. Givens is a tremendous defender with a questionable bat and the ability to pitch. He throws in the 90s from a sidearm delivery. He has a high ceiling, but the concerns about his bat probably hurt his stock more than anything.
Jake Barrett, RHSP, HS (AZ)
Barrett turns 18 in July, but already hits 94 on the radar gun and has a pretty nice secondary pitch in a power curveball that sits in the mid-to-upper 70s with good break. Last year, when the Rays took Kyle Lobstein in round two, many speculated that R.J. Harrison's Arizona presence was the reason. I don't know how true that actually is, but Barrett would fit the bill.
LeVon Washington, OF, HS (FL)
Toolbox! Washington has speed to kill. He's a line drive hitter right now, but a verbal commitment to the University of Florida pushes him down. Most have him as a future centerfielder although there are some question marks about his arm.
Todd Glaesmann, OF, HS (TX)
Another toolsy outfielder. Glaesmann was a two-sport star, which actually lead to a broken ankle that affected his season. He's got some speed, but his batting mechanics need work. He's pretty big though at 6'4", ~200 lbs.
Others
Mark Serrano, P, Oral Roberts
A lot of people will groan, but don't be surprised if the Rays don't bulk up on college pitchers again. Victor Wang's study from the past indicated they are the smart picks after the first round. Serrano has the numbers (13.8 K/9, 2.6 BB/9, 2.11 FIP) to make me swoon. He also has a ridiculous mustache and looks kinda like Andy Sonnanstine in the face. Good enough for me.
Austin Maddox, C, HS (FL)
Probably a second round pick, if the Rays decide against a first round catcher, Maddox would make a great consolation prize in the second.
Chris Gloor, P, Quinnipiac
He was on a horrible team and somehow managed decent numbers. He's a tall left-hander with a 90s fastball, a decent curve, and a change. Frankly, I can't wait for the "Little Place, Big Man" headlines to write themselves.
Hiram Burgos, P, Bethune-Cookman
Inferior competition, but walked 24, struck out 94. Reportedly has a good curveball.