Both of mine were from http://www.uktitaniumjewellery.co.uk/ – basic 5mm court band that cost about £30. I lost the first one on honeymoon in the sea, reordered the same but went down a size so it’s comfortable but snug and won’t come off by itself. I’ve got used to wearing it but have no desire to have something more expensive. It’s got a nice patina of scratches now.
Titanium isn’t that hard to cut, especially in the lower grades that they use for jewellery (and there’s no reason to have aerospace type hardened stuff on your finger). Harder than gold and silver and similar to most steels, and softer than most stainless steels. Tungsten carbide rings are too hard to cut, but any good EMT knows the technique of cracking them with some molgrips (it’s a very brittle material). Resizing can be an issue, but I think just because of the higher melting point. Not really a problem when they’re so cheap to start with.
I take mine off when I’m doing sports or anything possibly dangerous with my hands – just have a little carabiner on my keyring for it.