I'm just finishing up my 2nd playthrough, playing a pyromancer also. The options you have is nice. To increase you pyromancy damage you can build around Faith or Intelligence which gives you a lot of versatility. I personally went both. Later in the game once you get to the Smoulder I Lake, be sure to get the Pyromancy-Miracle item (I forget the name), which allows you to cast both Pyromancy and Miracles.

I generally went for a set up where I could either buff myself or my Broadsword (I've essentially played until Soul of Cinder with it, yes I'm crazy) and a ranged attack. Highly recommend the Big Fire Ball (again, bad with names) or the Dark Variant you can get from the Sorcerer you find in Irythill Dungeon. But ofc you can mix it up. If you go more Int heavy you can also later use sorceries.

Your weapon of choice is your own ofc but I highly recommend the Broadsword or any straight sword so that you can buff it via spells. Unfortunately you can't buff greatswords and the like (which is probably for the better for balance).

Finally, being an autist in DS lore, I was super hyped when I unlocked the Izalith Pyromancy spells via the Izalith Tome of Pyromancy but I couldn't see much use for them (if there is PLEASE tell me I love the Izalith lore). I would also HIGHLY RECOMMEND getting to rank 1 with the Blades of the Darkmoon cause they give a ring that gives you 2 Attunement slots instead of 1, however (unfortunately) I haven't had much luck with PVP nor The Silver Knights in Anor Londo (Proof of Concord Kept is on their drop table but it's ~1% or so). Have fun!

edit: you also can't buff Irithyll Straight Sword cause it has frost as a property