Ready to kick up my strength training a notch. Do I increase weight or reps?

Okay, general rule of thumb here, as far as reps go; strength training is basically teaching the muscle to endure contractile force over a period of time. This is half-way between power and endurance. Both fast and slow twitch fibers (white and red) are trained equally. As many people, even those in the "industry" don't know, there are intermediate twitch fibers, too. These fibers are essentially a combination of both, and are capable of using various fuels.

The ideas behind strength training are:
1) Work 'til exhaustion (failure or near failure) setting it apart from power. Power is speed! Power training will sometime utilize sets to failure, but this may become counterproductive.

2) Rep range shouldn't exceed twelve, but generally around five to ten (even eight). Powerlifters often do speed work in sets of threes, but these sets are rarely to failure.

Higher repetitions can be reserved for the latter portion of the workout. While this will invoke red fibers, the perfusion of blood, due to lactic acid buildup, will shuttle nutrients, growth factors, as well as hormones to the stimulated muscle groups.

3) Minimal warm up reps, but enough sets to be completely warm. What I mean by that is warmups should taper off in reps (ie 10, 10, 8, 6, 5- while the weight gradually increases) 'til you're warm enough to execute hard sets.

An example of that would be my deadlift warmups outside peak training:
135 x 10, 135x 10, 225x 8, 315x 5, 405x1, 455x 1 and the workout consisting of sets of 365-385x 6
I'd do as many sets as I could while maintaining that rep range, but working to failure- the last rep being the last rep possible. If my reps fall, my weight drops. So 385x 6 , 385x 5, 365x6 for 1-2 sets. My glycogen (stored carbohydrates in muscle {but mostly} the liver) stores are nearing depletion, so more muscle fibers (or different muscle fibers) are called on to complete the set.

With proper diet this will cause muscle growth. This is very similar to what a bodybuilder would do during a bulking phase (but eating like a fat bastard). These cycles must last much longer than the typical 4-6 weeks if you're trying to remain lean.

If lean mass alone or simply strength are the goal, your caloric intake must remain steady, and quite near your BMR, with protein and fats being the primary macronutrients. Both can be transformed into glucose by the body (liver) through gluconeogenesis.

Complete proteins and monounsaturated fats are your best friends here, but fibers such as soluble fiber must be incorporated (apples, chick peas --also high in branched chain amino acids, but a shit source of protein igeneral)and oatmeal are the best foods for those fibers)-- while meats (eggs are meat!), fish, poultry are the better protein sources. They also contain the necessary cholesterol for androgen production, as well as saturated fats for cholesterol and prostaglandin production.

Now, if joint pain becomes an issue, replacing some of the saturated fats with omega 3&6 fatty acids may help. These EFAs can help offset the arachidonic acid cascade, thus limiting prosataglandin production (very minor cell growth concession, but pains sucks! And pain outside the training halls isn't altogether needed). Muscles generally need to grow to gain strength (strength IS NOT power).