I fish a great deal with spinning rods/reels in sizes from UL up to MH rods with reels (all Shimano; mostly Stradics) in 750, 1000, 2500, and 4000.
I've tied lots of different lines looking for that one perfect line - haven't found it yet.
Anyway, braid does not seem to have twist problems and I like it a lot but I don't use it for everything because of my concerns with visibility (which not everyone agrees about). Closing the bail by hand, using a swivel, never reel against the drag, etc. all help but nothing cures line twist in mono, flouro, or hybrids completely.
I tend to think of the line on my spinning reels like gas in my car - you eventually use it up and need some more. ;-)
Also, I fish a lot of wacky rigs, finesse worms, weightless Senkos, and other kinds of baits that tend to spin on the retrieves - it's just going to twist the line and there's nothing you can do about it other than be prepared.
Never overspool your reel! If you put more line on the reel than you should, all that extra line is going to come home with you in your back pocket.
You might want to use some line conditioner spray, also. It does help a bit. Also, keep the lip of your spools very clean - same thing goes for your guides on your rod. Dried up pond gunk can catch on the line and create some problems for you.
Spinning reel lines need to be of the very limp variety - lots of stiff lines like some flouro and hybrids will just "slinky" right off the reel - much, much worse with smaller diameter spools.
Experiment! It's not cheap but I know of no other way to figure out what you will like. I use Trilene XL as my "base" against which I measure my satisfaction. XL always works very well until it gets twisted.
BTW - use ratings that are compatible with both your rod and your reel. I use 2lb. on my UL and never go above 12lb on my 4000. Mostly, I use 4, 6, and 8lb on my 1000 and my 2500. Yes, as a matter of fact, I have lost a couple of very large bass on those lighter lines but I catch a lot more than I lose and I still got to play those big fish for a little while before they broke off so, I'm a happy guy. ;-)