I use 10's on my Strat and 11's on my LP. That's the sweet spot for me. The same gauge will be slightly tighter feeling on the Strat, but the difference is not quite as much as changing strings size. The longer scale length only adds about a pound of extra tension per string.
Coming from Les Pauls, you'll probably want to set it up flat against the body. With it floating, the bridge will pull up slightly when you bend notes, pushing the rest of the strings a bit flat in the process. It also makes tuning up more of a pain too since raising the tension on one string makes the others go slightly flat. You have to keep going back and forth across the strings until they are all balanced out correctly. That takes some getting used to. On the plus side, vibrato sounds more natural with it floating since you can pull both up and down to wiggle the note. Finger vibrato is mostly subtle upward bends, so using the blocked trem for downward only vibrato doesn't sound quite the same. The trade offs are bridge lean when bending and if you break a string, your tuning is completely hosed. With it blocked against the body, it tunes and plays just like a fixed bridge. You often get better transfer to the body too which can give you a bit more sustain and fatness on some guitars. Just make sure you choose your bridge float position before you set your intonation. It's all interdependent.
I'm the opposite of you, I played Strats for many years and then got a Les Paul. One thing I will say is Strats are without question more comfortable to hold. Those body contours just hug you like long lost lover. Les Pauls and Teles sort of dig into you with their hard edges. Tonally though, nothing beats owning them all.