I am a young woman on her own living in Park Circle and I feel safe in 95% of the areas. The other areas are just ones that you don't wander by yourself into at night and you'll be fine. The Old North Charleston strip in Park Circle (East Montague St) has a good mix of ages and lifestyles out and about. There's a few bars and a bunch of great restaurants. A few of the restaurants do trivia which is a great way to meet people. There's no apartment complexes in the Park Circle neighborhood to speak of but there are rental homes that can give you a good idea if you like it here or not.
I lived in Summerville in an apartment complex prior to moving to the Park Circle area and, while it was a nice area, I found it hard to meet people up there. It's definitely a quieter town and, while I don't go out to party and be crazy, I just found myself wanting for more of a social scene. There are nice apartment complexes up in Summerville and it's a safe area but I personally feel just as safe here as I did there.
Hope you find luck with your move! If you have more questions please feel free to shoot me a message