What features should I consider when getting an ice cream or gelato machine?

You covered the big differences. Everything else is going to be brand and manufacturing quality.

My opinion on the different types:

For small amounts and small budgets I really like my cuisinart with the prefrozen bowl. The bowl gets so cold in my chest freezer that I don't even have to take the time to chill my mixture if I'm in a hurry. It always has plenty of cold leftover.

The ice/salt type either hand cranked (that's what kids are for) or electric are nice if you need to make batches back to back. You can obviously refill them instead of refreezing a bowl.

I don't have experience with the self refrigerating variety as they are out of my budget for the occasional homemade ice cream.

I have a Donvier brand ice cream maker. It's a hand-cranked kind with an insert that you pre-freeze. Unlike the old-fashioned salt/ice kind, the hand-cranking involved is super minimal, so don't necessarily discount that option. (Basically, you just need to scrape the ice cream off the sides of the insert occasionally, so it's usually something like crank it around 2-3 times every 5 minutes and it only takes about 20 minutes to freeze the ice cream.... you'll likely spend more time stirring your ice cream/sorbet mixture during prep, than you will after adding it to the machine!)

I would personally recommend this style since it means there are fewer components to break and they tend to be much less expensive. The pre-frozen container is part of what makes it so speedy, but obviously it means you can only make 1 batch at a time and it takes up space in your freezer. I think the only reason to get the kind with built in refrigeration is if you want to make multiple batches in a row and you plan to use it a lot.

Whichever style you choose, buy the largest one that your kitchen can accommodate since you can make a small batch in a big machine. I got mine at a garage sale and as a result, it's the pint size, rather than the quart size and it's the one thing I don't like about it.

If you really like ice cream and you're prepared to spend the extra money and accept a larger machine then in my experience you'll get better and more reliable results with a machine that has its own compressor.

I initially used an Andrew James machine without a compressor and top drive paddle and it only had enough freezing power for one 700 ml batch of ice cream mix that had been completely pre-chilled in the fridge for many hours and there wasn't any room for error with experimental mixtures that didn't freeze as quickly (e.g. mixtures with added alcohol). If churned too long the mixture started melting again. It also required the bowl to be frozen for 24 hours to work - 8 hours was not enough. Limiting churning power and pretty much impossible to stop churning to check the mix without risking it freezing solid, the paddle sticking and not being able to restart.

I've now got the Cuisinart ICE-100 and it's in a different league. Much more powerful churning mechanism and robust paddles. Longer warranty. The mixture can be churned from warm (well below boiling point for safety though). Completely consistent smooth results. Much less sticky frozen residue on the side of the cannister to jam the paddles. Removable bucket so the mixture can be added easily to the bucket without the paddle or lid in the way. Bottom driven paddles so it's easy to remove the lid during churning to allow warm mixes to cool more quickly, stop and restart the churning, add extra ingredients or check the results. The machine can churn one batch after another. No more than an hour to churn from hot to frozen per batch and much less for cooler mixtures. Highly recommended (disclaimer: I have no connection to Cuisinart and paid full retail price).

I've cooked large amounts of mix and churned the first batch from warm, the second from room temperature, the third from fridge temperature, the fourth after chilling in the fridge overnight - the texture and flavour are the same in each case in my experience. I think the point of the standard advice to leave the mix in the fridge to 'mature' is to make sure that the mixture is cold enough for machines without a compressor.

My only problem with the ICE-100 is that using the optional gelato paddle results in gelato that's so dense that it freezes solid in a standard home freezer after a day and can't be scooped. I think dense gelato with less air really needs to be stored in a higher temperature freezer or served within a few hours. I prefer the standard ice cream paddle. Any other owners care to comment on their ICE-100 gelato paddle experiences?