The screenshot looks good. I remember when the demo came out and I played it a bunch, it was really impressive. Not just the graphics but also how much stuff was happening on screen, and it still had great performance.

Probably something to do with scaling. If you have set your display to >100% scaling, some apps/games will do that.

if you can make application specific scaling rules, you might want to do that for proton/games and set it to 100%, I guess?

It's not quite a pistol start; the game gives you a set of default weapons on a per-level basis. I wouldn't call a fresh start something almost standardized like it is in the Doom community, though. The game is clearly intended for continuous play. However, it is also designed around the default weapons being entirely practical. In the end, it is a preference thing. I like the slight challenge boost.

For a first time ever playthrough, definitely choose Hard. Serious has double damage, which is real harsh if you aren't familiar with the general landscape and enemy behavior. Serious is well worth an eventual revisit though, since the extra enemies (and double ammo!) wildly change how the game plays out.

My other general advice is never quicksave mid-fight. Often you checkmate yourself long before you die, and it's really easy to save where, it may not look like it, but you've already lost.

You can have all sorts of fun in "Advanced Options > Advanced Rendering Options." The relevant settings for these are listed under "Rendering control." I don't believe you can disable mipmaps entirely, but using either Nearest Neighbor or Trilinear (according to preference) with 16x anisotropy (no point in going higher) will get rid of the obvious detail lines.

Note that nearest neighbor also affects things like lights and shadows, which might look pretty strange. The game is built with filtering in mind.