So this is how I usually play the game, it's by no means the "correct" way of playing, but optimized to how I play it and to the game's own issues.
I don't bother upgrading the axe. The axe is handy in the very first levels, but after that the dagger becomes my go to melee weapon IF I choose to go melee at all, because there's plenty ammo to go around.
After I get the pistol, I don't use the Staff ever again. There's no point in upgrading it.
Get the Magnum. The stock pistol is weak and becomes obsolete if you don't upgrade it, HOWEVER there's plenty pistol ammo later in the game, so you might as well use it. The Magnum packs a punch and shoots fast, so it's the ideal choice. The Flare Gun is nice, but Project Warlock doesn't have hitscanners that deal lots of damage like Blood has, so it's best to finish your enemies right away then counting on damage per time.
Sometimes I don't even upgrade the shotgun. The stock shotgun is good enough for me, but when I do I choose the Slugshot for the more consistent damage output.
My main use of the Double Barrel is against bosses, so the Harvester makes short work of them. It really makes every boss fight so much easier. As I said multiple times, there's not much point in damage per second in this game, so I'd rather not upgrade the Double Barrel at all than getting the Flak Cannon.
If the SMG didn't share its ammo pool with the Minigun, I would upgrade it to the Akimbo. The Nailgun is a gimmicky weapon that can hurt you, there's no point in getting it. But I don't upgrade the SMG at all, I save my unlock points on that one.
As for the Minigun, the game doesn't have long drawn out fights against massive hordes to warrant the Autoturret. Plus, the Heavy Bolter is so good, strong and accurate.
I don't upgrade the Dynamite up untill the last boss, that's when I pick the Frag Grenade. I use the Bomberman spell a lot, and for that spell the Pipe Bomb sucks. As for the Frag Grenade, the risk of hurting yourself while using it doesn't make it worth it. The last boss fight has lots of open space and many mobs to fight, so the Frag Grenade is usable in this case, plus the upgrade is cheap, so it's a good use for those last remaining unlock points.
The Supersonic Rockets are simply better. As I said before, damage per second don't make much sense in this specific game, this isn't Blood. Plus, the Supersonci Rockets are, for all purposes, a hitscan weapon (of sorts).
I don't upgrade the crossbow. I barely use it. In fact, I even forget I have it.
The Firelancer is neat, but the Heavy Bolter already accomplishes a similar job with much more plentiful ammo. The Spreader is best for handling multiple mobs at once.
One problem this game has is too many weapons, most of them with unique ammo. There's a lot of different types of ammo pickups for the devs to place around maps and that's why the Laser Gun ammo is the "rarest" of all (it's not that rare, but there's less of it than any other kind). So if I'm using this weapon, I need to make every shot count, that's why I choose the Rail Gun. Plus it's powerful and great against some mobs in the last episode of the game.
I use the Bomberman spell a lot. It's an offhand Rocket Launcher - you can fire an explosive projectile while holding another weapon. Plus it come early in game and it doesn't use much mana. If you're gonna use this spell, don't upgrade your Dynamite to the Pipe Bomb.
The second and last spell I use is the Sammoner. It's too useful to ignore, and frankly too OP. Sometimes there's too many mana potions around the map, so I just use it. This spell is absolutely essential at the last boss.