Transmission not going in gear right away, when I first start the car it goes into gear fine, but when I make a short run cut of and go back to start the car it doesn't shift I have to give it a lot of throttle for it to jump in gear

It sounds like the clutch packs in first and second gear are probably shot. Automatic transmissions are the weak link on all FWD vehicles. It's important to drop and clean the pan, change the filter, and replace the ATF every 30,000 miles.