I ran extensively with a non-jogging stroller. Well, extensively for someone with a very young baby, anyway. I had a Britax B-Agile. It runs about $200 and is much more lightweight than most strollers, especially joggers. It weighs 17 pounds, for reference. I ran on a paved, fairly flat path, probably four times a week with the stroller (and often on the weekend with my husband pushing it), distances up to about 5 miles, 9 mpm or slower most of the time. It's been a little while, but here's what I liked:
1.) Fully reclined so baby could nap. I normally ran during her nap time, so she'd sleep through the run.
2.) Single front wheel that locks
3.) Lightweight
4.) Excellent rain cover - critical in the Pacific NW in fall and winter. The rain fell and baby stayed dry and happy.
Jogging strollers often include:
1.) hand break - not necessary IMO if you're not running many hills. If you are careful and run mostly on flats, I don't think you need this.
2.) Tether - see above, or you could makeshift something
3.) Inflatable wheels - totally unnecessary for slow running on pavement
After I had my second, i bought a double jogger at great expense. I think it was probably a waste of money. In terms of the actual stroller, the main advantage was that it's tough to find side-by-side double strollers with a single front wheel. But we had moved to a really hilly area, and I just wasn't strong enough, especially in the first year post-partum, to push our two kids up the hills at anything resembling a run, and downhills felt hazardous.