I'm in a very similar type of league.  You are looking at spending over 1/6th of your budget on Vmart and Mauer alone (only 1/10th of the players you need)  There is lots of other offensive help for the other teams to pursue.  Pitchers are more valuable than hitters (9 vs 14) and the same amount of categories 5 vs 5.

My two thoughts in your situation would be, first, that Posada earned $14 last year, but that was more questionable the prior two years.  As a catcher going into his age 36 season I would be concerned that he is due for a fall.  Second, and, just as important, assuming that he is likely to be your third best catcher, you don't need him to be a catcher at all.  To the extent your league considers position scarcity in trading, you might be able to get a better hitter for him (e.g Frank Thomas) by trading him to someone who needs a catcher.  I think you are a lot more likely to do yourself some good this way, than by sticking someone with the 21st best catcher who might otherwise not be drafted.

Posada - he may be worth 14 but he very likely will not.  I would not keep him.  Let someone else take the risk.  VMART is max value.  He's keepable but weigh how $25 extra dollars can really help you improve two or three other spost in a big way.  I would rather have 1 stud catcher, find someone else cheaper (Zaun, Napoli, etc.).

Do not fill your DH hole going into an auction.  Keep it open as long as possible as it allows ultimate flexibility in bidding on any hiiter available.  It maximizes bargain hunting at the end.

Catchers get a lot of their value because they are hitting at a premium position, not necessarily because they are good hitters.  If you are using a catcher as a DH I think you are greatly overpaying for their offense.  Not taking their position into consideration but I bet you could find similar offense from  another positional player probably $10 cheaper, if not more.

Keep Mauer and Martinez, let Posada go.  I bet you will get better DH offense in the $14 elsewhere.  

Considering that this might be Vic Martinez' last year catching, I might look to move him while he is at his peak value (which is probably now), though that would depend on where your team ranks going into this season. If you are a real contender, keep him however if you are middle of the pack or lower, make the move because he likely won't be a catcher and his offense out of first base won't be worth the $25 you have to pay for him.