So I played System Shock, the remake, played some of Thief 1 and 2 and I was looking at the Ultima Underworld games because they seemed interesting. However, I know they were built around limited mouse movement and have a... interesting HUD. My question is for a new player who's never even played an Ultima game and is used to more modern HUD and controls, is there a source port or fan patches that make the game look and feel more modern? Or do you get used to it after playing it?

I wanna try these Ultima games cause they were a big stepping stone to System Shock and the like but I'm intimidated.

First, for the sake of clarity, let me note that the Ultima Underworld games don't at all play in the same manner as the other Ultima games available here on GOG.

Thus, don't let your conclusion regarding Underworld affect your decisions regarding the other Ultima games!

Anyway, to answer your question, the closest that I know of (at least that was properly playable last I heard) is "Underworld Exporter". See the following forum-post for more on that!

https://www.gog.com/forum/ultima_series/underworld_exporter_play_ultima_underworld_in_unity_with_mouselook

The controls are somewhat different from modern convention, but they still function well enough. Anyone could adapt to it if they wanted. If not, modding in mouselook is an option.