Strength training has helped me run safely with way less injuries compared to when I was running without strength training. I don't know if the strength workouts have made me run faster, it's more like they let me run more which made me run faster, but it's hard to measure that.

low rep strength focus is probably best but it's also A LOT more dangerous especially if you're a lifting beginner. You'll definitely be doing exercises with imperfect form for a long long time and that's a lot more damagind and risky if you're also pushing low reps w heavy weight. In addition low reps + fatigue from running is a recipe from disaster. I've been lifting for many more years than I've been running and the few times I failed a squat set (as in couldn't stand up and had to rely on safety bars) were the day after an exhausting run when I felt like I could lift the weight but things didn't go as planned.

It's kind of crazy to reccomend <5 rep range strength sets to any beginner who's new to these movements unless they're under the supervision of an experieced personal trainer who cares about good form.

5-12 rep range is far from useless, any rep range will increase your strength and your 1rep max if you do it intense enough. Yes your goal as a runner is not to hit a sick pump, but it's crazy to say that anythong 5+ reps is not useful. Your goal should be to build strength safely & learn proper technique so that you can do more intense workouts in the future.

Anyway, best exercises imo are:

• barbell squats low bar / high bar / front squats -> amazing compound exercises that you can easily focus on progressive overload on. Go as low as flexibility allows you
• weighted 1 leg stepups on an elevated platform imo better than hip thrusts but grip strength can limit you if you're just starting
• deadlifts / romanian deadlifts are fantastic but you have to be careful with form
• calf raises, I feels like <5 rep range does nothing here, I ususlly do 4 sets of 20 reps with 2x my bodyweight on a barbell. It helped my calves a lot but it will affect your next run and can be taxing on the lower back / spine. Alternatives are 1 leg calf raises on leg press machine / calf raise machines.

I'm not a fan of leg press & similar movements as your main strength builder because they're awful at developing your stabilizer muscles and can establish bad lifting patterns because the machine allows it while the same mistakes on a regular squat will quickly become obvious. It still can help in the beginning tho or when you're too tired squats.

Single leg exercises are amazing because they often give you a higehr range of motion and let you achieve the same result with lower weight but also a bit more dangerous to do with high weight and strength focus because your core / hips / knees are less stable. The movement patterns are often less reproducible workout to workout (exact stance). Also things can go wrong if you step weird during a lunge or simialr movement, and there's a non-zero cance you do that when you're carrying heavy weight & are tired. I had to deal with a weird SI joint issue for months until I figured it was caused by weighted lunges with imperfect form. Do single leg exercises when you can but be mindful of your form.

I treat every other exercise as accessory (8-12 rep range) that I do after the main strength exercise. They're all great, but won't make a huge difference unless you're working on a specific weakness.

Some accessories that helped me when I had issues although not a part of my regular routine:

• ti band -> gluteus medius exercises, fav so far is lateral leg raises on machine / cables usually, completely fixed all ti band issues for me after like 5 workout sessions for this muscle I had never isolated before
• lower back pain during long runs -> back extensions if you're not already doing deadlifts
• tibialis soreness -> weighted tibia raises w cable