Put it this way I'd rather have Firmino upfront than Benteke, nothing against Benteke I'm sure he'd be excellent for say a Chelsea, but for us it would mean altering our style significantly to get the best out of one player rather than buying a player who fits in with the rest of the team and elevates them. In terms of a DM, Rodgers has never actually ever signed one in his entire tenure here no reason to think he will start now, someone like Kondogbia would have been ideal, Lucas will do an ample job when fit (statistically,defensively only Matic and Coquelin are better) but it seems to me like Rodgers stumbles in to playing him there every season rather than it being out of choice, I think as you say someone like Illaramendi would be his ideal player in a holding role.
The main issue that still has to be addressed is the back four, signing different players isn't going to improve it by itself. There needs to be a coherent strategy in place, do we play with a high line or do we drop deep and the whole team needs to be accustomed to either method, not like last season where we had Sakho and Moreno playing on the front foot and Johnson and Skrtel dropping deep. It leaves massive gaps between the midfield and defence which were and have been consistently exploited in a Rodgers back four.
We'd be looking bloody good on paper.