Also, with the UA flight (assuming you have your BP), after you enter the general arrivals hall, go back upstairs to departures, walk to the left toward the Int'l G pier (gates 91-102) and if the security line is short, use that one. There is a passageway to T3 just to the right after the security checkpoint. If the line is long, just walk landside to T3 to the appropriate checkpoint.
I really don't know if UA has automated kiosks by their Int'l check-in counters (the last row of counters before the G security) but if for some reason you don't yet have your BP, check there first. (Yes, despite my 1K handle, in the past 4 years my UA flying has consisted of one LAX/SFO segment earlier this year.)