I believe they now have to offer roaming within the EU for no extra cost (at least until we leave anyway). So I wouldn’t worry about that.
If you want all the bells and whistles - 4G calling, WiFi calling, HD voice on 3G, highest speed 4G, etc, etc - then you’ll need to go with one of the four main networks who actually own their own infrastructure.
If you’re not bothered about all the extra stuff and don’t mind a basic calls, texts and data service you’ll probably get a better deal from one of the virtual networks like Giff Gaff, ID, Virgin Mobile…
I’ve been on Three, EE and Vodafone in the last few years. For me, where I live (south coast), Vodafone has been by far the best for coverage and 4G speeds. I get 140Meg speeds on a regular basis on speed tests.
I found EE was good, with pretty similar (maybe a slightly stronger signal in terms of ‘bars’ in some places - which is mostly meaningless) coverage to Vodafone but their plans were really over priced.
Three was alright, but a phone with their firmware on it so you can access their 4G calling is pretty vital to get anywhere near as good a signal as you’d get with Vodafone or EE.
Was on O2 too, years ago. At the time it was a bit crap and they were really slow to roll out new technologies.
(I’m currently on Vodafone SIM only. Unlimited calls and texts and 50GB data for £30 a month)