As black I found the Be2 lines in the Taimanov difficult. White can choose a solid setup and it is very difficult to gain something against it.

MilenPetrov wrote on 11/13/08 at 19:15:28:

I agree long theory is not the answer. We do indeed work on general chess understanding mostly (as well as calculation and time management). But I can't just do nothing when he happily plays 2.Nf3, 3.d4 and gets slaughtered again and again. Really my aim is merely to reach relatively safe positions, between move 7 to 15, where I can leave him to think on his own, maybe with some standard plans for both sides in his mental toolkit.

@zoo You describe the problem perfectly. Maybe I should recommend the 4 Knights as Black!? Actually 6.a3 is not completely stupid; it was recommended in "Dangerous Weapons: The Sicilian". White can delay castling (maybe go long) and play an early f4-g4. I am seriously considering this. Another option to make it really easy/non-theoretical is to just go 6.Nxc6 bxc6 7.Bd3 and play chess. This is an inferior 5...a6-Taimanov, but at 1500 level who cares?

I think that instead on focusing on long variations at this level u should focus on general understanding of the ideas, plans and pawn structures. What is the idea to teach him to remember 15 or 20 moves of theory when someone will devert on move 6 and then he/she should think himself. So better avoid these long opening variations and concentrate on general chess understanding.

a first advice would be to propose 1. e4 c5 2. Nf3 e6 3. Nc3 rather than 3. d4, as this cuts off some options for Black while keeping the possibility to play mainline sicilians.  

In the 4 knights, the Sveshnikov can arise after 1. e4 c5 2. Nf3 e6 3. Nc3 Nc6 4. d4 cd 5. Nd4 Nf6  when White plays 6. Ndb5 allowing 6...d6 7. Bf4 e5 8. Bg5 etc. If you don't want this, you can propose 6. Nxc6 bc 7. e5 Nd5 8. Ne4 which is a 4knights mainline.

In the Scheveningen proper, the classical main line with Be2,Be3, a4, Kh1 suggests itself ; a rich opening for both sides, your student is sure to learn a lot of things (not just moves) if she takes this path.
You can perhaps complement this with the equivalent Be3,Be2 against the taimanov, aiming for the famous (and straightforward) line with Bb4 Na4 (check which) ?

Against an early ...b5 by Black, just play like in Experts with Bd2 & a4: very sound, easy to play and to understand.   

On a final note : unless your student is concerned about making too many draws against Leko or Radjabov, why avoid the sveshnikov ? there are many lines where White liquidates the queenside and Black has to run after a draw with a pawn less in a drawish endgame (if he plays well), not much risk for White at any level here.