Help Me Refine My Weight Training Regimen

You would see better results if you lifted less and ran more. If you really want to lift 3 times a week, then do a day of chest and back, a day of shoulders and arms, a day of legs and overall body strength (dead lifts/ kettle bell training/ etc.).

Recovery from what? You should be lifting 7x/week and minimizing running. Haven't you heard running is the "dumbest" form of exercise.

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Most elites only put in one or two light weights sessions a week to prevent injury. A combined gym circuit session that includes pilates, light weights and core drills once a week is fine. This should supplement your twice weekly sessions and the Sunday long run as part of your schedule.

Don't get hung up on weighths and consentrate on running the hours and miles required every week!

Not quite the Hulk wrote:

I’m a 5k guy, so I’m not looking to build a ton of muscle, mostly just prevent injuries. .

How will doing bench press, biceps curls, and triceps extensions "prevent running injuries" ??? I really don't think they will do much in that department. They might help your arm carriage, and power when sprinting, and possible some effect on core, but, I don't think your program is giving you what you are looking for.

As far as lifting to prevent RUNNING injuries, one would need to be focusing on lifts that target the muscles/tendons/joints that get injured when.... running. Calf, achilles, hamstring, knees/quads, glutes, "groin", etc... in other words, leg lifting. There could be more of focus on this in the off-season/"pre"-season (base period), and could be scaled back during race season. So basic (nothing crazy) half squats, deads, knee extensions (be careful), hamstring curls, calf raises, and then maybe advancing to some explosive lifts like power cleans, power clean and jerks, snatches, and then finally plyos. Of course there is a catch-22 in all of this, that while these exercises can be very useful for building running-injury resistant legs, they (especially latter ones) also can be an injury risk themselves. One needs to be very cautious.

However, they are certainly a lot more specific towards what you want to accomplish, and will do a lot more in preventing a hamstring pull, or getting runner's knee, then will doing the bench press and some arm curls.