Usual advice is to get as big a machine as you have space/access for – assuming you're not purely into tiny workpieces e.g. watches/clocks. Bigger/heavier usually means more rigid which means better suface finish and/or bigger cuts. As well as being able to accommodate the ever bigger things you will inevitably try to machine on it!
As that sold items ebay link shows there's no need to rule out a Bridgeport-sized machine on cost grounds alone… condition is another matter… and completeness. If it needs accessories (e.g. for horizontal milling), make sure they come with it…
Do you have space for a floor mounted machine or does it have to be bench mounted? There are some quite compact floor mounted machines and these do tend to be a bit more 'serious' than the bench type – and you're more likely to get nice features like power feeds etc built in. Some of the bench mills are ideal for small scale work though.
Won't give names as could be here all day. Instead would suggest that whenever you come across something within striking distance that takes your fancy, look it up on the lathes.co.uk archive. That'll often give you an idea of how well it's regarded, if it has the features/travels you need, any known issues and how the different models of that machine differ. Also an idea of the age of whatever you're looking at… then you could always ask again here too.
Note also that many of the bigger machines will be three phase – unless you're confident with adding an inverter (not hard usually) it might be an idea to stick to single phase ones initially, so you can be up and running straight away. But also bear in mind that using an inverter (single phase power in, three phase out to a three phase motor) is actually the preferred situation for many users – you get smoother power, gentle start/stop and variable speed at the twist of a knob.
Buying secondhand does mean that you need to be able to assess the condition of what you're looking at, to a degree at least… but that can maybe wait for another post. But I wouldn't be overly worried about this – so long as all the functions work and it's not atrociously worn you'll still have vastly better milling capacity than on the lathe. Just don't spend too much at first. Use whatever you get for a bit and then you'll have a much better idea of what to look for if/when you want to upgrade…
The (entirely valid) argument for buying new is that you won't be working around a possibly worn machine while trying to learn the ropes. However, you'll get much less machine for your money, and I rather like using quality older machines that represent the golden days of manual engineering, even if they are a bit past their prime… the castings and worksmanship can be things of beauty, not something you can usually say of the modern imports… and a little wear is much less of an issue than it's sometimes made out to be, especially if you can fit a DRO…
But it's a hobby after all so just choose whatever floats your boat 