the best continuation... really I don't know but if I had to play it, would be Rd1

the best solution

Tb7Txb7axb7Tb8Td1Cc2Txd7Cxe3Ad6Axd7Axb8Ac6Ae5Axb7fxe3

Amateur

I agree with Vincenzo. The main variation runs as follows: 1.Rb7, RXR 2.aXR, Rb8 3.Rd1, Nc2 4.RXQ, NXQ 5.Bd6, BXR 6.BXR, Bc6 7.Be5, BXb7 8.fXN, ... and with best play White should win.

Amateur

I think the answer is probably 
 
1. Rxb8 Rxb8 
2. Rd1 Nc2  
 
{ 2... Nf3+? 3. Bxf3; 2... Rd8 3. Bb2 Nc2 4. Rxd7 Nxe3 5. Rxd8+ } 
 
3. Rxd7 Nxe3 
4. Rb7!  
 
{ 4... Rxb7 5. axb7 and the pawn queens; 4... Rd8 5. fxe3 wins a minor piece; 4... Ra8 5. a7 Bd5 6. Rb8+ Kf7 7. Rxa8 Bxa8 5. fxe3 and white is a piece up and an easily won endgame; } 
 
1. Rb7 looks strong too, but not sure if black is really forced to capture the rook on b7. For example, 
 
1. Rb7 Qd5 
2. Qxh6 Bf7 
 
and the game is far from being decided. Also if you play Rb7 first then try to transpose to the immediate Rxb8 variation there's a slight difference. 
 
1. Rb7 Qd5 
2. Rxb8 Rxb8 
3. Rd1 Nc2 { Now 3... Nc2 actually saves black } 
4. Rxd5 Nxe3 { Now white doesn't have 5. Rb7! to save the rook with tempo. Black is also actually threatening to play Rb1+ on the next move and might be even winning. }

Amateur

Mr. Dexter's in-depth analysis promptly corrected my obvious inaccuracies in drawing the main line of the position. Thank you.