1: Re-sign Tek to a 2 year contract.
This makes more sense than it sounds like. Varitek's chances of a bounceback year are greater than nil, especially if you can find a way to take some lefthanded at bats away from him. This is the option that is the least risky from a clubhouse chemistry perspective
2: Promote Kottaras, Brown, or both (platoon) as the replacement starting catcher.
Basically, replace a position that has very short major league depth from the farm and hope for the best from a pair of rookies at a crucial position. It's got some flaws, but it has the advantage of being, by far, the simplest and least expensive option to implement.
3: Scoop up someone's disappointing veteran (ex: Johjima) and hope they turn it around.
I like the idea of specifically Johjima, since he's in his prime (32,) he's got Clement breathing down his neck and his performacne was marred largely by a BABIP about .070 lower than his two previous years. That, and Seattle has a lot of holes that we can fill with spare parts. It's a solid big-market move.
4: Trade the farm for someone's successful veteran
This is probably the least good option, since successful veterans require a large load of prospects and usually have a contract on top of that. It does have the charm of having the best chance of being a move that grants us an effective catcher.
5: Trade for a young player.
Younster-for-youngster swaps don't really work very well. The Rangers will be looking for young pitching, but I think they want guys who are more proven, especially if it's going to be Teagarden on the block and not, say, Laird. It's a good way to pick up an inexpensive player but rookies can be pretty volatile.
In order of the way I want to do things, I'd say:
Promote rookie
Trade for Johjima
Re-sign Tek
Trade for young stud C
Trade for established veteran C.