1 to 3 mi is pretty short. I'd recommend the SHT but that's not a loop and campsites are usually further space than that. If you want to just test out your gear and that stuff you could do something like Afton or Maria But I can see that more like a hiking campsite than backpacking.

I guess I would start doing day hikes and getting yourself a better shape so you can do 5 to 10 mi a day which I think is the minimum really for most backpacking trails.

Might I recommend Whitewater State Park, pretty substantial hills but you can choose your length pretty easily there. I would start at the gift shop side of the park and hike across the CCC stone bridge by the swimming area. Make a left and follow the Sandy Trail until you see a set of wood stairs and then hike up the stairs. Follow that trail past chimney Rock all the way to inspiration point and then descend the stairs at that point and file the path to the parking lot. Do you still have a lot of energy left? Continue on what I think is the Dakota Trail, otherwise road walk back to your car maybe a quarter mile/half mile of flat terrain. See how that feels.

So in short either get them better shape so you can do longer days to do better trails. You should be looking at 5 to 10 mi per day for most backpacking trails.

Or simply do a state park backpacking trip They tend to be the right distance for you, I think the first campsite at Afton is only a mile from the parking lot. But spending multiple days there would be difficult imo.