I've had this game since launch but haven't progressed past the third or fourth level because every time I think about playing I get this rush of anxiety over the collectables. They actually benefit your character hugely so I feel like if I miss them I'm going to be under powered on not have as much fun. I also don't want to have to spend forever in levels figuring out the last few hidden spots because some of them are hidden pretty well.

Can I safely skip most of them and still be decently powered?

You can skip a lot of them. I ended up sticking to several weapons and a lot of the suit upgrades are kind of superfluous.

That said I did enjoy looking for them.

May slightly depend on your difficulty level, but you can skip past them if you want. I wound up re-playing levels to get some of the collectibles. You can re-play levels and anything you gain carries over while not re-setting your progress.

The map made finding the stuff pretty straightforward (Most of the time) I liked finding them and the upgrades, while not needed, are much appreciated near the end of the game or a harder difficultly.

You'll gather enough naturally running around.

You don't have to hunt for them, even on nightmare.

Although the ammo rune makes everything a lot easier since it will replenish your BFG ammo and the midair adjustment of your jump rune is just fun to use.

I 100%ed Doom, and had 22 weapon tokens left over. I think that would allow you to completely skip all secrets in the whole campaign and still upgrade all your weapons if you did all the challenges.

On the other hand, there exist exactly enough suit upgrades, so you do need to seek those out.

Most of the collectables are relatively easy to find, and there are clear/logical paths to get to them. The runes are definitely the most important thing, because they can really tailor how you play the game to your liking. I found all of the runes, and most of the other collectables in my playthrough, but I missed several of the hidden portions of original Doom levels. Those count toward the secret/collectable count, but don't really offer anything of substance to the playing experience. If you're missing those, you're not missing out on much (unless, of course, there's something I'm unaware of by also having missed several).