This is not correct. Ghost is open source software. You can download a copy and install it wherever you like.
The team that makes Ghost is also part of Ghost Foundation, which offers Ghost Pro (sites with domains .ghost.io), which is a paid hosting product. That’s probably where the confusion is coming from.
So, you can pay the team that creates Ghost (the open source software) to provide managed hosting. Or you can pay someone else to host the Ghost software for you. Or you can download a copy of the Ghost software and install it wherever you like, paying whatever it costs to keep that server online.
For newsletters, be aware that Ghost is pretty tightly integrated with Mailgun. If you want your newsletters to go out through your own SMTP server (which is quire possibly a bad idea, but that’s not what you asked), you’d need to make changes to the core software. You’re allowed to do that (it’s open source!), but it won’t be a trivial change.
How much does Mailgun cost? $35/month for 50k emails on their foundation plan looks about right, if you’re going to send one newsletter per week.
A Ghost plan for 10k members looks like it’s $99/month, for unlimited newsletter sending (to those 10k people). If you do a daily newsletter instead of weekly, Ghost Pro’s pricing is possibly better than Mailgun’s.
(Smaller newsletter senders: You probably want the pay as you go plan instead. On their not-really-advertised “pay as you go” plan, you get 1000 messages per month free and then $1/thousand messages. (https://help.mailgun.com/hc/en-us/articles/360048661093-How-does-PAYG-billing-work-) )
Before you decide to self host, make sure you’ve got the technical expertise to do it, or the willingness to learn. If you end up paying someone to help with server administration for a couple hours, you’ll quickly use up any savings gained by self hosting. This forum does lots of community support for self hosters, and we’ll try to help you if you get stuck, but if you’re going to need a LOT of help, you might be happier paying for managed hosting. It’s a question of trading time (yours to set up and administer the self-hosting) vs money (paying someone else to do it).