If I really want to use cheap off the shelf frames and mats, you should really always use a mat, just to keep the print off the glass, I will crop to the easily available aspect ratio.
For me that means printing 16×12 and framing with a mat in a 20×16 frame. This is fine since I can get 16×12 prints at only £1.15 each, plus £5.00 P&P. I then use frames the come with the mat that cost between £7.50 and £9.00 from either the Wilkinsons or Cherry Lane chains here in the UK. So as by doing this I can get the framed print cost down to under £10 I'm quite happy cropping to match a different format.
If I wanted to go to a 3:2 format then yes I can go to a 18×12 print, but I don't really like having twice the width of mat running on the long edge to the short, which would only add about £4 per item for the custom cut mat, if bought in bulk, or over £10 for small quantities. To get back to a frame with an even mat around the edges means going to a custom frame, and that will mean the frames costing £30 to £40! Since these are for personal use, and the occasional gift, keeping the cost under control is important to me.
Remember also that in general paper sizes for different uses have developed over time, independent of camera formats, of which there are also many. Most PnS compacts, and phone cams use the 4:3 format that matches the 16×12 print format I use. Also remember that if you want a constant width mat all the way round the image, the frame will be of a different aspect ratio to the print. My prints are 4:3, while the frame is 4:5.