CAUTION!! I GOT TOTALLY CARRIED AWAY HERE!!
Depends on how hard you plan to go with conditioning, how hard your barbell training is, what tool you plan to use for conditioning, how much you eat, how much you sleep, and how old you are.
If you're prioritizing getting strong under the bar through progressive overload, you don't want to do anything that adds soreness and makes recovery more difficult. Exercises with minimal eccentric component accommodate this goal better than those with high eccentric loading. Prowlers, rowers, bicycling, walking, OS Crawling, and hill sprints all have minimal eccentric work. Depending on age, you can get away with maybe two sessions of such things as long as you approach it as complimentary to your barbell work, rather than as goal-oriented, stand-alone workouts. I have found that, even at Age 52, a non-crazy* Prowler session once a week is beneficial to recovery and keeping body comp from getting outta hand. But I'm only under the bar twice a week in the 4 consecutive days I have to train. Maybe something like 3 sessions every 2 weeks would jibe with your M-W-f program.
*Non-Crazy: about 50lbs on the thing, on asphalt, 9 rounds of 20 seconds work/100 seconds rest.
All that said, keep this in mind. Getting strong takes a very long time. Getting much stronger than you are now (if you're a relative novice to the barbell) can happen very, very quickly - IF you allow it to. "Allowing it to happen" means, adding weight to the bar, being diligently consistent, eating an excess of calories with lots of protein, prioritizing sleep, and (errmahgerd!!) sacrificing your stunning abbzorrs - for a season. Adding 200lbs to your squat is an impactful thing, worthy of a bit of sacrifice. If you put on some fat along with all the muscle you'll (inevitably) add, it'll come off extremely rapidly when the time comes, not leastly because you'll be handling much heavier weights during whatever activity you choose to use for that purpose. Getting back "in shape" for whatever sport you prefer is a very rapid process. Not "pro level" shape, but "way beyond most people shape" and very, very far from "unhealthy" shape.
I would encourage you to consider focusing on one thing and going at it to the best of your ability. In this case, get strong under the bar, then use your new strength to clean a heavier weight, do complexes with a heavier weight, push a heavier Prowler, generate a buttload more average watts on the rower, whatever you do - you'll do with more badassery.
And lastly, (I promise I'll shut up soon) you may be surprised how tenaciously your current conditioning level stays-put during your barbell strength focus. It used to be common wisdom around here that strength carried conditioning along with it for a very long time. I've found it to be completely true in two different "modalities" to borrow a phrase from the Crossfitters. First, in prep for my SFG, I did a snatch test in 4+45 with whatever my "walkin' around" fitness was. Then I embarked on 8 weeks of Geoff Neupert's "Kettlebell Strong!" double kettlebell clean & press program. Low reps, many sets, ZERO MetCon except for the cleans. After 8 weeks of no dedicated conditioning, no high-rep ballistics at all, I tested my snatch test again: 4+45. Secondly, I began the Starting Strength Novice Linear Progression one year ago: Big 3 lifts plus presses and cleans, for 3 sets of 5 except the cleans which are 5 sets of 3. No conditioning of any sort, lots of food, 20lbs of weight gain (232-252, I'm not small). In June, I decided to press "Pause" lose the weight, and do some conditioning. The Prowler is supposed to KILL PEOPLE. I eased into it just a bit, but was very quickly - think 3 weeks max - I was pushing the thing with 230lbs on it for 9x25 meter sprints in 15 minutes. More maximal strength makes repeated sub-maximal efforts much, much easier and there's just no way it can be otherwise.