I live in Melrose and have done so for the past 10 years. Always made to feel very welcome and very much part of the community.
I moved here for the biking and quickly started riding with locals to get to know both them and the trails. Social / community now revolves around the kids. Towns like Peebles / Melrose and perhaps Kelso are a little more ‘cosmopolitan’ in the way that they do not expect you to be 6th generation before you are regarded as a local!
The railway will make a big difference to how the area feels, in a positive way.
Crime is very low and although the comment above about drugs may be true, I can honestly say that in the 10 years I have lived here I have not been aware of, or impacted by, any drug issues.
BR is right though, employment is the big question mark for most people but again, the railway will make the commute to Edinburgh much more realistic for anyone wanting to work there.
We lack some of the city ammenities like choice of resturants, larger shops but you will not hear any complaint from me about that. There are masses of sports clubs, festivals, sports events and, where I live, a genuine sense of community. The schools are good and Council and Health services also generally pretty good
I love the Borders. I think the balance of rural yet not remote is perfect. The biking is world class, it feels like an outdoors /healthy place and I am glad my kids are growing up here.