Newbie Question about Upgrading Weapons (PvE) and Build Tips

Tried to make the title as explicit as possible.

So, in the case that I only wished to play PvE and not competitive PvP, would any piece of armour/weaponry be mandatory? Or would I be able to make do with most of the stuff available?

My main character (about to finish the game, just got to get three more Lord souls) is using a +4 Lightning Uchigatana, +9 Balder Shield (switching for a +4 Black Knight Shield against fire) and Havel's Set (when I can't equip Havel's Ring, I don the Silver Knight set, except for the Helmet - I use Havel's). My build is mainly melee-pyromancy. Any recommended piece of equipment?

P.S: Can't find the Eagleshield, would it be better than the shield I'm using right now?

P.S 2: Sorry about that moderator notification, misclicked.

So long as it's sufficiently upgraded you should be fine using just about anything for PvE.

It depends on if you are going to be doing NG+, Co Op, what exactly is your goal?

For your first playthrough that is a solid set, though you should upgrade that balder shield for more Stability, to +14. As you don't really need a slab.

The Uchi is pretty good with your Pyro, as if you fight enemies, such as in the Demon's Ruins, who are resistant to fire that will still hit them for a decent amount. Havel's set is good for most situations, though I've got to ask are you fat rolling, medium rolling, or DWGR rolling?

As well how upgraded is your Pyromancy Glove?

Yeah, I'm planning to keep upgrading the Balder Shield. Seems pretty solid.
I'm medium rolling (got Havel's Ring and the Ring of Favor & Protection, or something like that). My Pyromancy Glove is technically +19, since I already got it to +15, and then bought +4 levels off the Swamp Witch.

And I'd like to start a NG+ at least; dunno about staying on a certain level. People normally recommend to stay within the 120-160 SLVL, right?

PS. Totally not related with the build, but the Tomb of Giants is my next destination. Just to keep that in mind.

Do you have yourself a Sunlight maggot? That will make the TotG a lot easier.

Levelling doesn't really matter if you are planning on just playing Solo, for Co-Op Sl120 is easier, and SL120 is the common PvP level zone.

Alright, ventured without a Maggot, and got killed twice by falls. Both times I said to myself "It's fine, I already lit the bonfire in the Tomb."
Yup, I had lit it. I had not rested at it. Yes, each time I died it was aaaaaanother trip through the Catacombs. But killed Nito in my first try (you ain't no Capra Demon, Nito) and now I'm going through the Demon Ruins.

Thanks everyone for your answers!