I suggest you start by buying a nice jacket - a jersey blazer or something like the below (which I've just ordered but not received/tried on yet). If you like wearing jeans, you will feel smarter with a jacket I think.
YY to the jersey blazer. With better jeans and some simple tops that would be a really easy place to start. Maybe some ankle boots too?
At 5'8" and size 10 I think you will have lots of choice of things to make you look great. What shape are you OP? Which bits of you do you like best? Are there any bits you prefer to distract attention from?
I don't think you'll look "muttonish" in most things because you have the figure. Mutton is more about trying to wear clothes that look younger when you can't carry them off (with a middle aged spread or legs that haven't aged well etc).
Pick a style you like and cover up any obvious aged bits. You'll look amazing. Have you got a good hair style though? Reckon that's as important.