Google Maps shows it as a 1 hour-1:40 trip, which seems like a good estimate, though it can vary depending on whether there are accidents or breakdowns on the bridge. Waze predicts about 1:15 at that time. When you get to SFO, you could do a quick check of Google Maps on your phone for a real-time estimate.
Uber's fare estimate tool says $43-$55 (this will depend a bit on where you're going in Berkeley). With a $2 base fare, 75 minutes @ $0.22 minute, 28 miles @ $1.15/mile, and a $2 booking fee, that's $52.70. I think there's also an SFO fee of around $4, and you'll have to pay the driver's return toll of $6.00. Lyft should be approximately the same price. At SFO, Uber and Lyft are only allowed to pickup on the Departures level, so you'll need to go upstairs from baggage claim for that.
I don't think surge pricing is particularly likely, as I've personally never seen one at the airport, but it apparently does happen sometimes. I'd have Lyft installed as well, so you can compare (Lyft is quite popular in the Bay Area).
Instead of SuperShuttle (which sounds pretty miserable making lots of stops in traffic), you could consider a Lyft Line or Uber Pool, where it will try to match you up with someone to share a ride, though you may go out of your way to pick them up or drop them off. The amount of luggage you have may make this option impractical, but you can look at the price for a regular ride or a Line/Pool ride when you open the app and decide whether it is worthwhile.
As Nate sugguests, I'd still give BART some consideration, but its utility will depend in part on where exactly in Berkeley you're going. While the train will get extremely crowded later on, it will be empty at SFO, and you can change to what should be an uncrowded Richmond train at San Bruno (the first stop after SFO) and ride that all the way to Berkeley, about 50 minutes. You can take a (expensive) baggage cart almost as far as the BART fare gates, so this should be feasible if you're able to maneuver your luggage at all. Once you're on the Richmond train, you can get a seat and build a little luggage fortress around yourself before more people get on. BART will cost $9.45-$9.60 from the airport to Berkeley, depending on which station you get off.