Update: So if you run the server locally and select maps, you're presented with this screen, saying you need a key from openmaptiles.com: https://i.imgur.com/NTb5zIL.jpg.
Docs for building the tiles yourself are here [0,1]. It's worked really well for me so far. If you want a visual example of self hosted tiles, you can check out my (in progress) website [2]. The tiles are all hosted statically in S3 with cloudflare as a proxy, so it was pretty cheap.
Thanks, I will look into that. It's not altogether clear from their site — their Docker image basically implies that you're supposed to use their pre-existing datasets, which aren't free.
It's a little unclear to me. But from what I can gather, the basic software can download data from OSM, but if you want hillshading or satellite, you have to get that separately, and it's part of the $1,000 "production package" [1], which is actually $2,048 for businesses, plus $1,024/year for updates.
I have a couple open source repos for generating hillshade and contours (raster and vector, respectively) that I use with my self hosted tiles at nst.guide. The data sources I'm using are US only, though SRTM is a common choice for international Digital Elevation Models.
Forgot to answer about styling. Yes, looks like custom styles with the production package (which has hillshading, which ends up making the maps look much nicer) is much better. For some reason their main demos don't show off their best map styles.
Where did you find the $1000 quote? I know you can have them hosted unlimited for $245/month but I was fairly sure it was free for self-hosted use.