Hi Ellie,
Definitely agree that Etsy is a fantastic place to start. I did exactly the same thing with selling watercolour paintings. It's got a lot of great built-in features, particularly if you're considering offering customised options for paintings. Buyers can send you details of a potential custom order, and then you can reply with the various details/specifications/pricing etc. It's also really geared towards people looking for handmade art/crafts to buy.
Etsy does charge a listing fee, and takes a commission when you sell an item. If you link it to a PayPal account, they will normally take a % as well. There's also your postage/packing. I'm based in the UK, and offered free UK postage, and then c.£4 to everywhere else.
After fees, for a £20 sale, I'd normally take home approx £12-14 of that, so not too bad.
Perhaps after building up quite a bit of sales and online presence through those channels, it might be good to transition to your own site, with a purchase/checkout function. That way you'll be able to retain a larger amount of the overall sale value.
Equally, no harm in having other online eComm platforms running at the same time. Certainly Shopify would be good. Maybe Not On The High Street as well. You'd just need to track when an item sells on one platform, and unlist it off the others.
When you've got the shop up and running, send us some links - it'd be great to see your art!
Hope that helps,
Joe