Duson covers the situation pretty well. The 3 main considerations you must consider when in a shove-push/fold situation in MTTs is: 1) your stack size in proportion to the blinds + antes 2) your position on the table 3) how the action has proceeded to you and who acts after. (The third consideration may be moot if your stack size requires you to go allin because of it proportion to the blinds+antes.)
In short stacked situations, you can use push-fold charts as Duson indicates, and there are few that can be downloaded off the net. There are also
Apps & programs that allow you to do a few hand analysis of push-shove situation each day for free, such ICMizer + you can buy the programs. So, if you're short stacked there are times you will go in with far less than pairs, suited broadways, etc.
The other thing that springs to mind is that every poker hand is highly situation dependent. Going all-in with AA UTG with no-one calling you because you have a tight image isn't going to get you max value. OTOH, shoving AA in a loose table where people go are prone to calling with any Ax or broadway is going to often get max value for your hand. I suppose there really is no such thing as a favourite pushing hand as you need to consider all the factors in that particular hand in one time and place.
good luck on the felt