Newb and getting my 2016 "Leveled" Can I run 33's w/out any rubbing

Hey, I've a quick question about tire sizes for my Tacoma and a little background on why I need it.
I fish in ponds that don't have any kind of concrete for ramps and I've been stuck WAY to many times. To Un-Stuck my situation I've opted for the 4WD TRD Off Road pkg and I'm looking to get her leveled and mud tires installed to best defeat having to wear muddy socks home again.
That being said, does anyone have a best-size/tread/style of a tire that works for mud?
My budget for tires is $800 installed. I'm new to Tacoma's so hearing from owners that have been in my situation is a good idea. I'm not interested in anything that's going to affect my warranty.
Also; does anyone's acceleration seem different (I've got 4k miles on mine). This is my first experience with the Atkinson Trans so feedback is important.
Thanks for taking a few minutes.