LX2, buy your own External USB 3.0 HDD would be about the best box for you in my opinion if you are sticking to your in budget
Lets you record one channel and watch another, decent spec, good first box, miles better than going budget as most then sell on and upgrade once they see it all working, make sure you have a shotgun (double coax) cable
coming in to your house.
Also, if your router is near your TV straight Ethernet feed, if the router and TV are in different rooms
you will need a pair of homeplugs, plus you will have to pay a sub to a server
As you can see, you get what you pay for and it's easy to keep adding to the list of features :willy nilly: