You'll be fine with what you have if you set it up properly.
Neck relief - Mine is set so there is a gap about the width of a credit card. While holding down the first fret on the E string (low F) and the last fret on the E string (using your right hand), sight the gap that should appear in the middle of the neck between the top of the fret/s and the bottom edge of the string. I get that gap down to the width of a credit card, providing a slightly straighter neck for better action.
Action - I aim for a 2.5 mm gap from the top edge of the last fret on the G string to the underside edge of the G string (may need a little more gap on the the thicker strings). As soon as that is set, I set the rest of the strings to follow the radius curvature of the neck around the same action height. If any fret/string buzzes out anywhere badly, raise that string until that buzz becomes manageable and set the rest of the strings to the same action height and follow the curvature radius of the fretboard. That's as low as the action will get without too much buzz to deal with.
Strings - For slap stuff, medium light round-wounds, usually a .40 on the G string set I find is a good balance and nice tension for different thumb techniques. Can go up to .45 if you like, try .40 first imo and thicken the tone up with E.Q. and a little more volume. I don't think your looking for flatwound tone and tension for slap here.
Work on your style, I aim for a lighter slap style, not too light, but not the Flea type thwack
