Ours is grade 2 listed, conservation area in a world heritage site. It means things like doors and stuff are more expensive. Insurance is more expensive, but not massively so – find a normal insurer who will cover it (with a massive rebuild cost) – grade 2 is covered by most comparison websites. Mortgage companies are happy as long as someone will insure it.
More of a problem if it’s in a flood risk area, because then you’re combining flood risk insurance with listed building, which makes it a nightmare and hardly anyone will insure.
Long term maintenance things like doing the roof or doors and windows are quite expensive, especially if you have to get odd materials, although that can be the same in just a conservation area.
If you want it to be what it is, I don’t think it’s too bad – you have to accept that you’re not going to be bunging a massive extension on the outside of it, or pebble-dashing the front or whatever, or anything that changes it all that much externally beyond keeping it in nice condition (although with ours, because it is a terrace, people have got permission to do a fair few extensions at the back where it isn’t visible from the road, within quite strict limits though).