What makes a good film camera?

It depends what features are important to you.

As you say, you can think of a camera body as a pretty simple thing. It is just a light-tight box to hold the film (or sensor). If you go shopping for one, there are obviously many choices, and like anything, you just compare features (depending on which are important to you) and pick one that fits your budget.

First consideration for film photography is film size. Are you going to be shooting 135 film? Then narrow your choices to a 135 film body. Do you want a camera that advances the film automatically? Do you want autofocus? What metering options would you like? What exposure options do you want? Is full manual exposure OK, or do you want program exposure modes? Do you want a built-in flash? How many frames per second should the camera be able to shoot? Do you want multiple exposure capability? What about exposure compensation, and automatic bracketing?

How does the camera feel in your hands? What about robustness? What environmental extremes do you need the camera to be able to handle? Is the camera in good working condition? If it breaks, what are your repair/replacement options?

Manufacturers made camera systems, i.e. not only bodies, but lenses, flashes and other accessories. What is the availability of these items for any camera body you are considering?

Do you want to be able to use camera movements? If so, maybe 135 film photography is not your best option.

Take a look at the Nikon F6 just for comparison purposes. That's Nikon's last flagship 135 film body, and about as advanced a film camera as can be found. Have a read through the sales brochure / features / specifications and see which features look appealing. It will give you an idea of the possibilities, and then you can look for a camera within your budget that has the features that are important to you.

Great answer by osullic about the camera end of things, which to be fair IS what the question is asking about.

BUT, I would say it is the knowledge level of the person using the camera that is of paramount importance.

Knowledge concerning light and how FILM records it differently then human brains perceive it.

How the direction or placement of the light can effect the mood of the subject and effect the cameras Light Meter.

Knowledge of how to override the the cameras light meter suggestions in situations that the brain has more info then the camera. ( which is often in my experience )

Knowledge of F-stops (aperture) and focal length and how they affect depth of field.

Knowledge of the film you are using, it strengths and limitations and how to manipulate the development time to suit the adjustments you MAY have to make when you expose it outside of its optimum latitude. ( pushing or pulling your development time when you have less than optimum ASA film or want to have artistic license to be creative.)

Unlike a digital frame, a film frame costs money and resources and cannot be instantly reviewed. In the end, you want the camera that you can handle most reliably without needing to double check results, wasting the least frames. Reconsider using any feature great at "perfectly nailing or perfectly ruining the picture" (spot metering, unless you are very secure in its usage, comes to mind).

Some automation features (autofocus, matrix metering, TTL flash) that some would consider optional in a digital environment can help you waste less frames.

Features (like fully-automatic, subject-specific modes, "chip card" systems) that were aimed at snapshooters and minimizing required skill at the cost of available control will not likely be interesting for you, and could actually create wasted frames if accidentally activated.

Looking into how viewfinder coverage plays into the film workflow you want will potentially help your composition - you might want 100% coverage in a film SLR if you are scanning film strips straight, 95%-ish if you are projecting framed slides, and whatever works best with the printing workflow you use if printing (or ordering prints) from negatives.

Precision (lens mount, focusing screen and film gate alignment, shutter and meter accuracy, autofocus accuracy if using autofocus) and reliability in the camera build certainly will help. Otherwise, the camera body does not matter that much for image quality (excepting some rare innovations like the vacuum-assisted pressure plate in some Contax RTS models) - it is usability and ultimately style you are looking for.

Mind that a camera designed for informed-manual operation (eg a Minolta SRT-303) will be optimized for that handling mode ... and with some practice, MUCH quicker to handle than eg the manual modes on an autofocus-oriented SLR.

For me (shooting 35mm film in the 1980s through the 1990s) I enjoyed working with cameras that were mechanically well made and had a good selection of lenses that I could afford.

If a camera was mechanically well made, it was more likely to have good ergonomics and have precise controls that gave me confidence in what I was doing. A well made camera will also be more dependable, which is another confidence builder and frustration remover. The selection of good but affordable lenses meant that I could experiment with different lenses without spending too much money. A Leica has great dependability and is mechanically well made but I couldn't afford to get a second lens, so I didn't end up owning one for long.