It’s a nice enough area but isn’t a coffee-shops-and-nighttime-economy area, if that’s your thing.
Noise and traffic: it shouldn’t be particularly busy. I don’t know if Woolstone Road is classed as a main road but I would describe it as one step up from a quiet residential side road but not as busy as a B-road. It’s certainly not as busy as the South Circular to the north or Perry Hill to the south.
Public transport: 75 bus route runs along Woolstone Road (Lewisham-Catford-Sydenham-Penge-Norwood Junction-Croydon). There are 2 or 3 routes along Catford Hill. For trains you could use Catford (Thameslink), Catford Bridge (SouthEastern service to Charing Cross - but not a particularly good frequency), or Forest Hill (Southern service to London Bridge; and London Overground). The walk to Catford along Catford Hill isn’t the prettiest walk in the world. You’d have a longer walk to Forest Hill than I personally would want, but it depends what you’re used to.
Shops: there are a few small shops on Perry Hill (and also at the junction of Woolstone Road and Perry Vale) but definitely not of the trendy coffee-shop variety. There is however a GP surgery and two pharmacies at the end of Woolstone Road, so they would be almost on your doorstep! For supermarkets, the nearest are at Bell Green (walking distance) with a Sainsbury’s superstore and also a fairly new Aldi. A bit further away there’s a good Lidl on Southend Lane (better than the high street one in Sydenham) and as Pea said, Waitrose in Beckenham but you’d need to drive there. Catford has Tesco (but not large), Lidl and Aldi.
For independent shops and restaurants etc, you could explore Catford (which is never going to make a good first impression but has some OK aspects), Forest Hill, Sydenham and Stanstead Road/Brockley Rise. If you use a bus to get around then realistically you’ll be orientated towards Sydenham rather than Forest Hill, because there’s no direct bus from that end of Woolstone Road to Forest Hill.