At the moment I tried ZDoom (normal invisible monster) and GZDoom (translucent ugly invisible monster).

The problem is that all I want is to play vanilla-like Doom in high resolution full screen with GUI for ammo, with normal Doom effects and absolutely no blood on the walls or bullet holes. And I can't find the way to switch those effects off.
Important note: invisible monsters must me distorted as in original game.

Depends on levels you want to play.
If those are for vanilla engine or limit-removing ports with DEH-enhancement at most, you have a choice of PrBOOM and DOOM Retro. Chocolate DOOM and Crispy DOOM will give you trueЪ DOOM feel and look in full screen. But they have limited resolution of the internal renderer and lack GUI overlays for ammo an armor -- statusbar only. Check yourself what is more suitable.
If levels are for BOOM family or/and BEX-enhanced no choice but PrBOOM.
If you want to play relatively new ZDoom feature-dependant levels there is no other option than stick to (G/Q)ZDoom and seek for a mod wich could disable advanced visual effect on those ports.
There are not actively maintained ports as well (like EDGE), which might or might not have the features you are interested in. Testing is needed.
And don't forget to set when available 'Fuzzy effect' in graphics settings of the ports. That's traditional 'invisible' monsters effect you whish for.

--- Update ---

Screenshot examples for Crispy, PrBoom+ and Retro with HUD in the actual game. Looks like Retro too has limited internal renderer resolution.

you could try zandronum. it have a lot of different options.

You can really make gzdoom pretty DOS like if you play around with the settings. For a purely retro experience though my vote is with chocolate or crispy doom.