1994 Toyota Celica Weird Start Issues

I recently replaced my battery, and a connecter that was corroded as well as a terminal. I also recently used lucas stop slip to repair my trans slippage. The lucas helped, the battery works great. But now I have this issue where I will go for a drive, the car will start fine and get me to my destination, then I go to get back in and start up and my starter wont even turn over, but I have plenty of battery so I know its not a power issue, I tried giving the solenoid a little beating to see if it was sticking and I got back in my car and the same, no click no turnover at all, like a security issue, but I know thats not it cause I know how to disable that problem and it doesnt help, BUT a minute or two later after groaning and having a smoke and my car will start perfectly no fuss. It recently started this weird starting issue and I dont want it to NOT start on my completely. Its ok because for now I just wait a minute or two turning the key and ill get it, but it bugs me that my starter isnt even turning over then just bam pops on. IM not so sure I wacked the right spot for the solenoid but. PLEASE give me some advice that I might check out to see whats wrong with my baby. I love this car.