"....so services like Godaddy won't be necessary". Actually they are. You need a registrar (ie, Godaddy and others) to "rent" a domain from the Government. You never actually ever own a domain. They simply won't let you have a domain or TLD that isn't registered via an accredited registrar. You can always transfer registrars though, for a small fee. You can also "transfer lock" your domains so that others can't try to move them. That is the only way they can be "locked" to a registrar....but even then it's an operatorsoperator's choice.
If you are looking for pure cheap, then look for Godaddy coupons and transfer it out when it's time to renew it. Sometimes they do $1.99/yr domains for first year. But as mentioned by loads of people, Godaddy isn't that great.
The best alternative in my opinion would be Google domains. If only for the free privacy shielding...those spammers are very annoying.
The registrar you choose may or may not have a zone manager that functions. This is dependent on what name servers you choose to use. Once you get the zone linked to nameservers, you can edit the routing a bit. A raw domain is just an A record in the zone manager pointed to an IP, where the request will be picked up by a server. Subdomains are the same way. The www is actually a CNAME of raw domain. And MX mail entries can be either. Indeed you can use your home network and nameserver(s) if the IP stays the same (static), otherwise it will be constant upkeep of your A record(s) to keep it pointed to the right IP.