Definitely south welling, rather than north. Bexleyheath is just down the road. Nice roads there too. North Bexleyheath (meaning north of the tracks) is OK too - The Pantiles, Brampton Road, round there and over to Pickford Lane etc.
In ye olden times, the BNP had their HQ in Upper Wickham Lane. That's the bit of Welling that's mentioned, if you're concerned.
Welling is duller than a dull thing, though. It does have 2 supermarkets (Morrisons and Tesco), some North African/Mediterranean supermarkets.
The part of Welling which is just near Westwood Lane, Welling Way, over that direction is OK too. (Actually, just looked back through thread and someone else has mentioned them).
I've lived in the area for 45 years, so know it quite well..... 