I'm new to these forums but I've done a decent amount of strength training and read a lot on the subject so I think I'll be somewhat qualified to respond.
For most people new to strength training, a compound lift/linear progression routine such as Starting Strength is usually recommended. This consists of 3 short-ish sessions per week focussing on a few compound, all-round exercises and constant progression in functional strength is the goal.
A typical SS routine would be as follows:
Alternate workouts A and B....
Workout A:
3x5 Squats, 3x5 Bench Press, 1x5 Deadlift
Workout B:
3x5 Squats, 3x5 Standing Overhead Press, 3x5 (vary according to ability) pull-ups
You start the exercises quite a bit lower than you can initially manage to get used to doing the movements, work on technique and build your base, and you aim to put the weight up on each exercise ever workout. All exercises are done with a barbell and free weights. This means that every exercise works not just the muscles that are taking the main load, but your body as a whole, especially your core.
Exercises like squats and deadlifts have got a pretty bad rep because people injure themselves doing them. They don't deserve this rep because they are perfectly safe as long as you follow good form, which does take practice. There are tons of resources online for learning good form (SS wikia page with info on all the lifts: http://startingstrength.wikia.com/wiki/FAQ:The_Lifts)
This routine is aimed at any novice strength trainee (a novice in this case doesn't have any negative undertones, it simply refers to a person that can make regular workout-to-workout progression on their lifts). However as you're obviously doing a lot of other training (ie your tri training) then you can modify the program to fit with your routine. It will work almost as effectively if you only do the routine twice a week (eg A on Monday, B on Friday).
Hope this helps.
Btw, there are tons of different routines that people will suggest, and many will work, but in my experience and from all the reading I've done, SS or a variant is by far the most efficient method of gaining all-round functional strength. I've known a lot of people move on to SS after years of ineffective gym programming, and I've not known a single person be disappointed.
Edited: 05/10/2012 at 15:06