Here's a little overview about framing. It's a whole world of its own, so it's generally a good idea to bring your etching to a frame shop and compare the frames directly next to it instead of ordering one immediately.
Glass frame + passepartout
So this is the usual go-to way of framing etchings. Do decide on a budget first because for each component (frame, glass, passepartout) there's different quality grades. The most important thing to me is the frame design (wood colour, width etc) and the passepartout colour. When it comes to passepartout colour, I really recommend comparing the paper of the print to it first, so wait until you have received your print until you decide. Nothing is more annoying than the colour being just slightly off if you're trying to have the same colour as the paper. For frames, it really just depends on taste.
As a rule of thumb, the inner passepartout cutout should be at least 2cm longer in width and length than the print so that you can then place the print in the center (or slightly higher than center) and you still get to see the title and signature under the print.
For example, if you have a 30x40cm print on a 38x52cm paper, the inner passepartout cutout should be 32x42cm and the outer passepartout format should be anything over 38x52 (say, 45x60 standard size) so that it fully covers the paper and a little extra for tolerance.
What's so great about this way of framing is that
1) it's independent of paper size, so you can get affordable standard size frames even for odd paper formats. Or a huge passepartout and frame for a tiny etching if you so prefer.
2) even if the print isn't perfectly centered (which happens because they're hand made and the papers are also hand torn) it can still be placed centered within the passepartout cutout.
3) you can choose funky colour combinations for any sort of interior design.
About age resistance
If you want to be super safe about age resistency when choosing frames, I would ask a framer or a company specialising in archiving materials. This is nerdy territory and you may or may not actually find a difference in the materials' effect on the print in your lifetime. The info I can give you from my side is the data sheets of the papers I use:
Fabriano Watercolour https://fabriano.com/en/product/watercolour-cold-press/
Both have ISO 9706 age resistency, meaning they're acid free and buffered with calcium carbonate against acidic withering.
The inks' pigments are bound in linseed oil (Charbonnel ink) or burnt plate oil (Gamblin Portland ink).
As a general rule, avoid putting *any* original artwork in a place where it's exposed to sunlight most of the day. Etching ink is usually very lightfast, but I would still rather be safe than sorry here. This also goes for places with very high air humidity, the paper and frame can suffer from it.
Alright, that's about all I can say on the matter. Hope it helps and that you find an awesome frame for your print! I absolutely love seeing how people frame and place them, so please feel free to tag me on social media or send me an email when you've got a photo of it :)