Apologies if this is a bit brief/ direct:
I would never buy the Unibrau system. I have one of their controllers, and the build quality is low. Their kettles look cheap to me, and that pump appears to be a $30ish dollar knock off from eBay.
Dozens of brews in, I love my system and if I was doing it again I'd build something like this:
Spike custom kettle with 4 TC ports- $320ish
Auberins EZBoil controller $370
Blichmann Riptide pump $200
TC 5500w element $75
Brewbag $25
Then connect everything with SS fittings as needed
In the end you'd have a much higher quality kettle with TC port that would allow your system to evolve in the future, a control box with a very user friendly controller, a fantastic pump with strong output, a TC head, and much easier cleaning, a solid element, and a simple BIAB solution.
You cannot operate a system like this with full volume boils on just 120v and expect a strong boil. You could always add a 120v induction burner under the kettle if you have a second 120v circuit and don't want to use your stove.