Note that LGB (Long Beach Airport) is about 20 miles further south of LA than LAX Airport...... most public transportation or shuttles are aimed at LAX..... you may find it much easier (and cheaper, faster) to get to LAX airport......so a $25 savings will not be worthwhile.

Also, there are many flights from LAX to SFO......few from LGB.....so if there are weather problems, you are more likely to get another flight from LAX with less wait than from LGB........ Actually, look to see how frequently Alaska flies from LAX to SFO compared to United or Southwest flying from LAX-SFO....with you tight schedule, you'll want to have many back-up options......keep in mind an alternate airport for SF is Oakland (OAK).....from the Oakland Airport, there's a 10-min ($3) bus ride to the BART transit subway station which goes into SF (the same BART system thath you get on at SFO airport)...... so if your LAX-SFO flight is cancelled, there may be less wait for an LAX-OAK flight....... enjoy!