Some people wear braces with other clothes than sports jackets or suits, but that places you in some subgroup that listens to swedish rockabilly or some such. Since you need to ask, I guess your friends aren't part of any particular brace wearing hipster community. Then do as Jovan says and stick to braces with odd jackets and suits.
If you have a pair of trousers that are most comfortable with braces, and are going to wear a thicker sweater, you can of course wear the braces underneath, if they don't show.
TM Lewin has a good basic selection, made by Albert Thurston which is the premier brand. Their navy/blue stripe is excellent. Albert Thurstons own selection is much broader and you can get some really nice braces with white 'catgut' ends, which IMO are the most elegant and versatile.
Avoid formal braces (unless wearing formal wear) and braces with little figures on them. I could wear some with hunting motif to tweed but they are much less versatile.
AT has some really good regimental striped braces. The red/green is very nice, as are the blue/golden yellow. For summer, the light blue and champagne pastel braces with white ends are great.
I like burgundy over red, with gold metal, but silver metal with blue braces.
Brace buttons are most easily affixed (on the inside) with a sewing machine, though I spin the wheel manually. Just remove the 'foot' and set it to the right stitch width and do 6-10 stitches in each pair of button holes. Stitching by hand is of course best but a tad boring.