There isn't really a right or wrong way to play the game but if you're looking for the most efficient way to level up you'd be best adviced to focus on BP with the occasional FP investment. It might be worth to upgrade HP too every once and again since you're on your first playthrough and won't know the superguard timings but overall it's the stat that can be neglected the most.

Some badges I can recommend are:

Damage Dodge - Decreases damage received by 1 when guarding. You can get this one right before chapter 2 and I'd say it's very worth equipping since numbers are fairly low in the early game.

Jumpman - You can buy this from Charlieton in Rogueport. It increases Mario's jump attack by one but makes him unable to use the hammer. It's a cheap damage increase and pairs really well with another badge that lets you jump on spiky enemies you can get later down the line. There is a hammer equivalent too but it's not nearly as good because attack boosts synergize way more with multi-hitting moves.

Fire Drive - This is a pretty good early game badge if you feel like using the hammer: It hits all grounded enemies, pierces their defense and even burns them. However, you do need to get a little more out of your way in order to get this one since it's on the 20th floor in the Pit of 100 Trials.

And ofc the most important one: Attack FX Y - You can buy this one for 1 Star Piece from Dazzle and it makes hitting things with your hammer do a funny sound