There are a bunch of things in the game that require lots of influence. The fusion core in your house for instance requires 50k influence to buy. You get there quickly if you're focusing on it or you can take as long as you want.
I usually have the fusion core before the first 6 months have elapsed along with a bunch of other things that cost influence like grenade launchers, the 2 extra lots you can buy to expand your house, some revital, etc. You can just wait to capture any of the abominations if you're worried about it. I frequently capture one from the area you find Laika and Loden on day 1 and just leave him unprocessed until I hit 6k influence so I can then add him to my house and sell him. It only takes 2 or 3 weeks to get to 6k.
I usually have the fusion core before the first 6 months have elapsed along with a bunch of other things that cost influence like grenade launchers, the 2 extra lots you can buy to expand your house, some revital, etc. You can just wait to capture any of the abominations if you're worried about it. I frequently capture one from the area you find Laika and Loden on day 1 and just leave him unprocessed until I hit 6k influence so I can then add him to my house and sell him. It only takes 2 or 3 weeks to get to 6k.