I have heard two of these concertos performed by my peers in my piano studio (doctoral students), often played every week for an entire term. I haven't heard the Mendelssohn concerto played live, but I know it well.
1. I think the Mendelssohn concerto is a fantastic piece. It is very fast, a great crowd-pleaser, and very ear-wormy. It is a brilliant show of virtuosity, and, like most of Mendelssohn's work, it blends seamlessly the aesthetics of late classical structure and organization with fiery romantic passion and enthusiasm. I actually will recommend this one first, since you have only a semester to learn it (that said, I don't actually know how fast you learn pieces so ...), and especially if you are a high-school or undergrad student, or don't have much experience playing concertos.
2. The Liszt concerto No. 2 is a beast. It is easily the most difficult one on this lis(z)t, just for the sheer danger of many of the runs, leaps, and glissandi. Liszt's pianism is evident here, but there are many places where he pushes even the techniques found in the transcendental etudes to an entirely new level; and there are a number of passages with scales in thirds alla the Don Juan paraphrase. There's a reason this piece isn't played much!
3. I actually really like the Prokofiev Concerto in D-flat, though I don't know its details as well. My friend won a concerto competition with it, and the hardest thing about it is not even the playing, it's the ensemble. As with all the Prokofiev concertos, the orchestra-reduction part is unreasonably complicated and hard to put together. Do you have an accompanist willing to play this for you? Give them the score immediately, it will take them quite some time to pull off, even if they are a professional! It is less extreme than the Liszt concerto IMO, though still fiercely technical.