DHCP is a really stupid* service for the most part. Unless you are working with multiple subnets or have some very specific settings you need to pass to your clients, it’s probably not worth it to manage it yourself. I don’t want to discourage you though! Assigning static IP addresses by MAC can be extremely useful and is not always an option on routers. If you want static names and dynamic addresses, that is really where you need to manage both DNS and DHCP. It really depends on how and where you want names to be resolved and what you are trying to accomplish. (*stupid as in, it’s a really simple service. You want it simple because when DHCP breaks, you have other serious issues going on.)
Setting up your own DNS is worth its weight in gold. You can put it just about anywhere on your network (before your gateway, after, in China, whatever.) and your network won’t even know the difference if setup correctly. You can point BIND at the root servers and bypass your ISP completely if you want. ISP DNS services suck ass, so regardless of you resolve yourself, or forward all name queries to your anon DNS server of choice you have a really decent level of control on your network. It is the service to learn if you want to keep an eye on where your network wants to talk.
Your Unifi USG must play nice with your own server, by the laws of DNS. There may be some nuances when it comes to internal protocols like WINS, but other than that, it should be just fine.
I would setup a simple VM somewhere first, to answer your actual question. It’s good practice to keep core services isolated on their own, dedicated instances. This is to speed up recovery time and minimize down time. Even on your home network, DNS and DHCP are services you do not want going down. It’s always a pain when they do go down.