I doesnt really matter. I started out with a softer one and moved to a harder foam roller once I felt like I needed one.
Try either running the day before squatting or after working out but not the day after (in fact, I would suggest not doing any exercise the day after to allow sufficient time for muscle recovery). Running or even sprinting the day before will not likely affect your squatting strength because you'll have the a day to recover. After working out your legs will be a bit sore but not even close to how sore they'll be the day after squatting (due to delayed onset muscle soreness). Experiment a bit because everyone is different.
Iron Junkie - Go Hard Or Go Home
I'm not trying to drag this out, but I think your comments are interesting in how they relate to priorities.
For you, weightlifting is your priority so sled dragging is an accessory to that, designed to facilitate the primary focus, but is less important in itself.
However, somebody who's taking up running in a more serious fashion may want to be in optimal condition for that training. I know that I couldn't go for a decent run the day after squatting because I'd be too wiped out to train hard enough, my technique would be off, and my legs would be sore. I'd also be potentially harming my squat recovery by attempting another hard activity the day after. I'd be short-changing both my running and my squatting. I might go swimming the day after squats bit that is a non-impact, non-weight bearing activity and so isn't as bad.
Now if running is your only sport and you run every day then you will likely have to run the day after weight-training. But it won't matter because you are so well-conditioned to running, and strength is so low-priority that it won't affect you. I think where timing gets more important is for the guy who's relatively strong, has strength as a priority and is also trying to run more seriously - then you have potentially conflicting goals and routines need some planning. You want toset it up so both are minimally affected by the other, and both activities can be trained effectively.
I used to run a fair bit last year, and due to the glorious weather recently I've started getting back into it - can you tell?