As a fairly recent arrival in St Margaret's I thought it might be helpful to add my experience here. We moved here early last year - just before Covid - from North London (Marylebone) and it was 100% the right decision - we love it here, even though with lockdown we've not yet had a chance to spend as much time out and about in the area as we'd like.
Initially we focused our househunting in the roads surrounding St M's village itself, but once we realised we'd be looking at either 2/3 bed flats with limited or shared garden space or teeny weeny cottages, compared to 3/4 bed Victorian terraced houses with large-ish (for London, anyway!) gardens north of the A316 we moved our search there and didn't look back. Obvs everyone has different priorities when househunting, and for some being in the village itself may be more important than square footage/garden space - but for us personally we felt we needed more substantial space inside and out. The house we ended up buying is perfect for us and we still feel it's miles better value than south of the A316. We live on Haliburton Rd, which is lovely and friendly, and have plenty of space to grow into this house over the years (I think if we'd bought in the village we'd have needed to move again in a couple of years' time).
In terms of access to parks etc. - this was my main reason for wanting to be in the village itself, but actually we're really happy with our local green space options in the end; our nearest park for short lockdown walks is the Old Deer Park just over the river, which is easily accessed from our house in about 8 mins by walking down to the river via St Margaret's drive then across the footbridge. The river path in both directions is also lovely for walking - either up to kew (past kew gardens on the right) or down through Richmond, Petersham and out to Teddington. It's also a nice easy walk from here to Richmond (15/20 mins using the footbridge) for eating out, shopping, cinema etc - (remember that?!) obvs when we're actually able to do those things again! 
I was also a bit worried about plane noise @BlindMelon123, but it's really not that bad where we are and after a while you get so used to it that you don't notice it anymore. Before living in Marylebone I lived in Putney for years, which is also under the flightpath, and I'd say it's about the same here - it certainly doesn't feel any noisier to me. Obvs it was lovely in the first lockdown when there were no planes flying, but being under the flightpath is way less disruptive than I worried it might be, and imo it's more than worth it to live so close to the river (which I love), walks, parks, all the great restaurants/cafes/shops etc. that Richmond, St M's and Twickenham have to offer.
Hope some of this is useful to those of you looking to move here, anyway!
I actually came across this post because I'm pregnant and am researching nurseries in St M's / Twickenham, so if anyone has any recommendations I'd love to hear them - thanks ladies 