Can you share some of the context and prerequisites of what you’re looking for?
If you know Gulp (or similar), for instance, I’d use Amazon S3 + Gulp + Cloudflare. That would give you very good performance, with a price that’s hard to beat (if that’s important for your project).
If you have a larger budget you can look into Netlify. A lot of people on the forum seem to swear by that host, but for me I find them too expensive for what they offer and am not very impressed by their speed.
But then again this depends on what’s important for you; if easy deploys through Git are important for you, you might want to give Netlify a shot. (Or use something like Wercker if you don’t like Netlify’s offering.)
I don’t know why you would do that. From the way I look at this, an additional domain gives extra work (in setting up, deploying each time, and maintaining), gives an additional domain lookup in terms of website speed, gives a greater discrepancy between the localhost and live site (so greater likelihood of errors), and is generally speaking unneeded in my book.
Perhaps if you want to use server software like Caddy or Apache to serve your static HTML files, then offloading the images to S3 or something can help for if your traffic grows in the future. (For now it seems unnecessary, since a good-configured server won’t have trouble serving static HTML and images to 10k daily visitors.)
But I’m personally quite pragmatic, so wouldn’t even bother with running an additional Apache (or something) server for static HTML and just use something like S3 or Azure for website hosting.
But then again, if server management is your thing and you have the time, energy, and budget for it, then by all means go for it. It’s after all your project, so you’ll need to work with the tools that you know, prefer, and trust – regardless of what we might recommend here.
Without telling us about the specific requirements, features or qualities in a host you need, we’re all just stating our own preferences. Here’s a spreadsheet (linked to below) with 15 hosts that are known in the static space. It might be outdated, and not strictly for Hugo, but will give you a sense of what’s out there. I’ve used about 3/4 of these and they all have something to offer.
Many of use like Netlify because they’ve automated many of the processes that are involved in hosting a static site, like cache invalidation, provisioning SSL certificates, and build-failure/success notifications, and their build times are really fast (which may or may not be important to you).
I also use Firebase hosting, which is fast, free, and has SSL certs. I have clients who want a large name brand for a host, so Firebase is a good option for them, because Firebase is part of Google.
Aerobatic has been adding some nice features lately, like integrated search and a control panel with traffic statistics. Also, aome of the content editing services, like Forestry are including hosting, so you don’t have to think about hosting. If you need or want to roll your own, AWS might be a way to go.
So, there’s plenty to choose from.
Full disclosure, I have either friendly or business relationships with some of the organizations above.
Usually when people put their photos on a separate server it’s to serve them from a CDN for performance reasons, but with a static site you can serve the entire site from a CDN, if you want to, so you don’t necessarily need to.
That said, I often use a service called Imigx, which allows you to call particular parameters (like size, image quality, tint/blur, etc) in a query string, which will help with performance. It’s not a free service, so may or may not be right for you. Imigx takes your images right from your site folder, so you don’t have to worry about uploading them to a separate service. Keep in mind though, that if you do keep your images with your repo you could end up with a big repo.