Ignore the other poster. We all start where we start. George Gandy and most of the top UK coaches would say that an international, elite runner who lifted (i.e. sprinters, Coe) might reach 2 sets of 1.5 x bodyweight with thighs below parallel - after several years of strength development. But if you take an average distance runner who has not lifted before and teach them to squat safely, you'll start them with a 20kg Olympic bar (44lb) and nothing more. Then they'll probably kick off around 50% of bodyweight and progress quite quickly to 75%.
For 800m, both pure strength and strength-endurance are beneficial. And you can get both from weights, circuits (stepups etc), drills, bounding and hill sprints. Many ways to do it. I would NOT lift to exhaustion if you are already in the middle of fairly serious running training; the time to learn is in the off-season.
If you do want to lift weights then I'd suggest...
1 'heavy' exercise per session: squats, deadlifts, split squats, front squats, Bulgarian split squats. Rotate through different ones, and make sure you do some 'legs apart' exercises as well as 'legs together'.
1 faster exercise: cleans
1-2 posterior exercises: Romanian deadlifts, swiss ball hamstring curls
Make absolutely sure you get instruction and learn the technique perfectly. This will help you avoid injury and be an asset for life.
Forget the bench. Pointless for runners. If you want some upper body work, do pushups, alternating with either chins or inverted rows. Both of these are good core/plank-type exercises as well as using some upper body muscles, and if you do both you get balanced development and can use them to kill time in the recoveries. You should be taking a full 3min between the sets of squats and deadlifts, so take 1min, do some pushups or chins, and then another minute.
Finally I would also make a claim for using hills. Many world class runners got there without picking up a barbell. Read up on Lydiard's hills. The benefit of this is that you combine strength/power with a running session, so don't have to juggle extra fatigue and extra sessions into your week.