So I'm coming at this from the opposite direction really. I've surfed since I was 12/13, 27 now. I surf at a fairly high level (I'm sponsored, for what thats worth, I don't get paid to surf but I get free clothes and surf gear, and I compete). I just got into lifting a couple of months ago, after a couple of shoulder dislocations and another couple of injuries I've been working with a top physio who basically got me into lifting to fix my imbalances and get better at surfing.
You probably need to decide on your priorities. The heaviest professional surfer currently on the tour (so top 34 in the world competitively) is around 180, maybe 190 pounds, and he's 6'3. There have been a few bigger guys, but they are generally only good in bigger more powerful waves. The greatest surfer ever, kelly slater, who is still arguably the best (at 43 years old) is 5'9 and 160. Half the top guys in the world are sub 160. Strength to weight ratio and agility are what you need, plus explosive core strength. You will see a lot of bigger guys who still surf well though, especially in hawaii where the waves have power the extra weight is less of a disadvantage.
Being sub 10% body fat but strong and flexible is way more important than deadlifting big weights, think gymnast not powerlifter. I'd never touched a weight in my life (I never even did push ups or pull ups) until 2 months ago and I was 'ripped' by most peoples standards, (although obviously I'm super skinny by this site's standards), first time I tried to do pull ups in the gym I managed 15, I did 10 pistol squats the first time I tried, it took me about a month to learn how to do dragon flags and one armed pull ups.
Point is that surfing for several hours a day is sufficient to get you in pretty good shape if you surf aggressively on a shortboard.. If you get 4 waves an hour on a longboard you probably aren't getting much in the way of training from it.
You also need to make sure your whole body works together as a unit. Isolation exercises are probably in no way beneficial unless you have an actual rehab reason. And stay flexible, a pistol squat touching your ass to your heel and with your knee staying well behind your toes should be easy and shouldn't bother your knee or your hips are too tight or your balance sucks..
My training consists of full body workouts twice a week, but I move it around depending on the surf, if its going to be good I won't hit the gym the day before. I basically do vertical pull/push and horizontal pull/push for upper body, plus a few other things, laterals and front raises, YLTWs and face pulls for shoulder health (paddling a surfboard really strengthens and tightens your internal rotators but does nothing really for your external, thats why my shoulders were hurting). I do back squat, but I don't go too heavy (usually around my bodyweight on the bar) since I squat slightly asymmetrically due to spending so much time standing on a surfboard slightly twisted, the more time I spend in the gym the more that is getting fixed.
People here like to bash bosu boards and the like, but surfing is all about how much force you can apply to a really unstable and constantly moving object, so I do things like pistol squats on the balance boards, I squat on swiss balls etc.
Long rambling post, hopefully there's something useful in there..