Exercising on Keto Diet

I would exercise as normal. If you feel like you are getting worn down or tired fasted add some good carbs (sweet potato, etc)

I find I don't really need to eat any different when I'm eating strict. My workouts aren't usually more than an hour and most of the time my body has enough stored energy to get through OK.

I'll skip the whole "you don't need keto to lose weight" and I'll assume your decision to do keto is an educated decision.

Standard keto diets tend to be fine for aerobic activity, although particularly long sessions (e.g., a marathon or a cycling tour) may require some carbs to help replenish your muscle glycogen. Anaerobic performances tends to suffer on a standard keto diet but many people find they do okay at first. To elaborate a bit, the issue you can run into with exercise on a keto diet is muscle glycogen depletion and anaerobic activities tend to be fueled more through muscle glycogen than fat sources (unlike aerobic activities which can largely be fueled from fat sources). You may find that your activity level isn't sufficient to deplete your muscle glycogen stores (which is the case for many beginning lifters and I'd say most aerobic activity) in which case you'll likely be fine to stick with a standard keto diet. If that's not the case, you want to look into targeted or cyclical keto diets (usually I'd say targeted, as it's less rigorous), which will help replenish muscle glycogen stores while still following a keto diet.

As for what exercise to do, I'd vote both strength and cardio but it really comes down to your goals.