Play the one you like! That's the answer. Great pianists are ARTISTS, not artisans.
Prokofiev 2 has to be a joke. #1. It's too long. #2. It's too hard. I think the first movement is among the best all-time when we're talking about classical music. But, let's face it, the other three are not exceptional. The second can be exciting, and the third and fourth aren't bad. But, the first movement blows the rest out of the water, making the concerto anticlimactic and much too long. When you're said everything that needs to be said in the first movement, you don't need three more tacked on. The first movement is a complete piece in itself. I think Prokofiev should have taken the other three and written a new first movement, leaving the original as a completely separate work.
If you're concerned about pieces that are overplayed, I agree with the selection of the absolutely great Rachmaninov 4th. But, only the original or 1927 version. The piece is so much richer and more lyrical in its original form, not the chopped-up nonsensical form the "final" version is in, where the ideas don't develop properly.
The Scriabin concerto is a great choice.
Tviett's 1st concerto is very nice. Most people here balk at the name because it's unfamiliar. But, it is a beautiful piece that deserves a prominent position in the Romantic piano concerto genre. If you like nature, you'll like the piece. It invokes Scandanavian fjords, waterfalls, lakes, etc. It's completely tonal and not typical Romantic-period melodramatic rubbish (like so many lesser-known pieces from the period). The downside to this piece is that it's probably too easy and too short. His 5th concerto is long and more difficult, though.
If you want something innovative/modern in character, check out Tcherepnin's 5th concerto. It's not terribly difficult and it's melodic, although chromatic. It's VERY under-appreciated. Unlike melodically-challenged modern concertos (Rautavarra, Schoenberg, Bartok's 2nd), Tcherepnin is both modern and palatable. He doesn't grind listeners down with horrible dissonance (Bartok) or murky-chewy sludge that goes nowhere (Schoenberg).