Here was my strategy in MR1: Get a new monster, feed it two or three packets of Sting Dust (acquired on the desert expedition), give it a Vitamin D, and then send it off to Training, since monsters get the same stat gains throughout their whole life in MR1. The Training grounds serve as the best place for stat boosts (the jobs can't compete). When they get back, give them Taffy until they're full of energy again, stick in another Vitamin D and a Mint Leaf, and head back to Training.

Once a creature trains past 300 in a stat, they'll take home a technique (generally). There are 6 techs given out when you master a course, 3-5 that you start with, and 1-3 that you pick up randomly on the courses. In order to get the Power and Skill techs, just let the Vitamin D boost those stats up to around 300, and then train once at the course to acquire the new move, while your monster concentrates on the Life, Defense, Speed, and Intelligence courses.

Once all stats are above 300, train out the rest of the stats to wherever you think they should go (try to have a mean average of about 450), and then freeze the monster until some tournaments come along to get back the cash you just spent on training and Vitamin D. Also, I didn't know that stress affected lifespan when I was really playing this game, so I'm sure that with it you could have monsters surviving at least another year or two. If you're lucky enough to find a Golden Peach on expedition, then don't worry about lifespan, because your monster becomes damn near immortal under its effects.

The results? I have one of each main monster sub-breed (except for Plant, because I didn't get around to re-training one after I lost that save file; Monol, because I didn't know about stress; and Hare, because I overdosed it on a barrage of drugs when it couldn't meet expectations based on being a Suezo sub-breed) with all 12 techs, all of which have one the Major 4, and all with stats at a mean average of about 450, which means that they can take down any enemy in the game. I may have to go back and raise one with MR2 methods to see if I can get a mega-super-powered monster, but I'm content with what I have.

nate's method is sound. here is my addendum: in mr1, all battles start off in long range. find your monster's kickass long range attack, develop skill + whatever type of attack it is, and hit them before they hit you. "one-hit" wonders are much more effective in mr1 than they are in mr2.