First and foremost, this guide assumes that you're already using Lemmer's 'Widescreen HUD Fix', as one of the console commands (crosshairsize) only gets added to the game with it.
1) Go to the 'bin' folder which is located under the game's installation directory.
2) Open config.ini with Notepad.
3) Add the following line first. Note that this line will hold your default HUD values and will bind what may be called 'HUD On' mode to G, with a FOV value of 120 and personalized crosshair / HUD sizes; so feel free to change the first three values and the key to your liking.

Cfg.Bind_G = "crosshairsize 0.4; fov 120; hudsize 0.5; showweapon 1"

4) Add the following line right after. This line will bind what may be called 'HUD Off' mode to T, with a FOV value of 130; so feel free to change the key and FOV to your liking, but do not modify the other values as they are crucial for the HUD-free look.

Cfg.Bind_T = "crosshairsize 0; fov 130; hudsize 1e-005; showweapon 0"

5) Save and exit.
You can now use the binded keys of your choice to toggle the HUD and the first-person weapon models on and off during the game, as well as going back and forth between the two different FOV values while doing so. The changed values will show up on the top left corner as HUD messages but they will disappear after a few seconds, leaving you free to take your shot.
Note that moving on from one chapter to the next (or switching to Battle Out of Hell) may delete one of the lines from the config file. In that case, just add the deleted line again or try setting the config file to 'read only' beforehand (which I didn't).
Here is the result with the above-mentioned values (which I personally use):