Normally a magazine will just take First Serial Rights for whatever country they are in. If so, then you are free to sell First Serial Rights for other countries to other magazines, or First Anthology Rights for the story to appear in an anthology.
Larger/more prestigious markets may take First English-language Rights (which leaves you free to sell the story in translation) or even First World Rights, but you'd expect them to pay you for publication if they want to have those rights. They may also have an option to reprint your story in an anthology. (F & SF specified that with the two stories I sold to them, though it was an option they didn't take up.)
Your own collection would have First Volume Rights, e.g. the rights to the whole collection, to be published as a book. (First Electronic Rights I'd assume would be the case for an e-book.) My own collection (all but one story previously sold) came out in 2003 and is now out of print, but if I wanted to resell it somewhere else First (British) Volume Rights had been bought by the original publisher.
If a market is going to put restrictions on reprints, then this should be specified in a contract which you will have to sign. For example, my contracts for the two stories I sold to Interzone in the 1990s ask for a year after their publication for any reprints unless a) the story is being expanded into a novel, b) the story is appearing in the author's own collection or c) the story is being reprinted in a Year's Best Anthology. If any of those apply, you had to request permission from Interzone, but the contract said that they would not unreasonably deny your request.
There are opportunities to sell collections to small presses in the UK in the SF/fantasy/horror genres, though in most cases it helps to build up a reputation with story sales first. As for major publishers - unless your name is Stephen King or Neil Gaiman, forget it.