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so, I just took timed diagnostics and got 143.
I got
LG 3/24
LR 15/24
LR 12/26
RC 14/27

It took me 30 min to do four game questions. I was only able to do the first half of LR and RC... seriously, why do they only give 35 minutes???
I'm hoping to apply this fall. I can study full time, probably 5hrs/day in May and 10hrs/day from June. I'll take Sept and Dec. tests. Hoping for 170+ score. Maybe I'm unrealistic, but if I get anything lower, I'll probably apply again next year.
I've been reading a lot about different books and courses. I think I'm going to go with 7sage for LG and Lsat trainer. I also have seen many people using powerscore, but I'm not sure if I should spend so much time on the basics when I have so my prep tests to go through.
So my plan would be
May~June: Lsat trainer for RC and LR + 7sage for LG. Build up some basic skills.
June~August: Prep tests

What would be the reasonable score increase? And should I add any more books? Any recommendation?

Instead of doing 7sage+trainer why not just do one of the 7sage courses? These courses cover LG+LR+RC, then if your not happy, you can do the trainer once you've finished the course. Ive gone through the trainer, and am now starting with 7sage's cheapest course

Def go with 7Sage and if you're still shaky on some stuff use The LSAT Trainer to get a diff perspective. They work well together but you'll probably just confuse yourself so I wouldn't do it. I used 7 Sage exclusively for LG. The LSAT Trainer had a few things I liked but I pretty much just breezed through those sections. I absolutely loved the Flaw sections and RC in The LSAT Trainer. The book is cheaper than the lowest 7 Sage course but I would purchase the lowest course and go from there.