Need help integrating weight lifting into cardio

A quick brief: I'm 24 and overweight. About 2 mo ago, I started running and cycling and I'm now at about 3miles/day at 10min/mile. I'm down from a peak of about 200 to 180, but would like to get down to 165. I haven't been doing any weight lifting but would love a short program to integrate into continued cardio as I'd predominately like to prepare for some longer triathlons eventually.

I haven't hit the weight room for about 10 years, so I remember almost nothing. I have access to a small gym w/ free weights and machines and would love help designing a simple program. I also don't have tons of free time, I'm a med student and should be studying 24/7 for a test coming up in June.

Thanks a lot!
 
3-4 exercises per session with a few warm ups and a few work sets is usually good for beginners, as keeping it simple and practicing a lot is the best way to learn the exercises. Free weights would be ideal as they're the more functional exercises (compared to machine weights), which is especially important if you want to do something like a triathlon.

I'd recommend a program that will have you learning and mastering the following 6 primary exercises:
- Squats
- Deadlifts
- Bench Press
- Chin Ups/Pull Ups (can be done with assisted machine until you get your weight down) or Lat Pulldown
- Overhead Press
- Rows

You might do all 6 exercises every resistance training day, but it would probably be easier to ensure you do them all with good form and progression if you do half one day and the other half the next day (eg A: Squat, Bench, Pull Ups, B: Deadlift, Press, Rows).

I'd start at a light weight and low reps, since your technique will probably fail long before the weight starts feeling heavy, and since endurance would be your primary fitness goal, it may be ideal to progress to higher reps moreso than higher weights (eg fortnight 1: 5 reps/set, fortnight 2: 8 reps/set, fortnight 3: 10 reps/set, and so on). But there is still merit to increasing overall strength, since a triathlon will most likely have you working against waves and wind resistance, which would be easier to battle if you have both strength and endurance.
 
You could do that and get good benefits as well, but I'm referring to exercises such as Bent Over Rows, Pendlay Rows, One-Arm DB Rows, Cable Rows and the like, in which you either bend over facing the floor and row a weight up to your torso, or use a pulley system to row a weight towards you in a more conventional rowing position.

Here's a quick 20sec vid of a Pendlay Row, to show you what I'm talking about:
 
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