What would change if we don't want an off-grid system?
I.e. use power from panels, and use AC/DC PSU for the shortage/night time usage?
Say i need to run ~120 W miner. Backing up with grid means id use 0 to 120W from grid... How to loadbalance keeping consistent 12V supply?
Well, you wouldn't be using the battery or battery connection cable... instead you'd be using a grid-tie box, and probably be needing to call in a licensed electrician to tie that into an auxiliary panel. You'd also need to get permit from your town to do grid tie, some small towns don't allow it under their code. The DC-USB converter would also go as well... you'd be plugging into normal power outlets.
Depending on your town codes, and power company, you might be selling any excess power generated at a set rate (usually less than the generation rate you pay for receiving generated power), ultimately reducing your bill while giving the power company cheaper power. OR, the electric company might have a pass from the town or state in which they do not have to pay for excess power from your grid tie (some do... which REALLY sucks, because then they're getting anything you generate in excess for free.)
Overall, the initial hardware outlay would be cheaper because of the lack of battery. Your maintenance over time would be less too, also because you wouldn't have to change the battery at end of life (approx 8-10 years.) However, your TOTAL cost over time using panel+battery would be less than using panel+grid tie, and that would be less than grid-only. The break even point between each is usually about 2-3 years. (Longer time to pay off if you live in an area that has a lower solar efficiency, and less amount of hours of sun in a day. Las Vegas gets more hours per day and more direct solar than Chicago, which gets more hours and more direct solar than Finland. Google Photovoltaic Map)