Beside hardware stores:
Our lumber yards will sell oak and poplar cut to the specific length you need ($4-$5/bd-ft). Home improvement stores generally don't cut to length, but can stock a good selection - we (Central Ohio, USA) have oak, walnut, maple, hickory, poplar, and a few other hardwoods on the shelf.
Try local custom cabinet makers - they have a lot of cut-off ends of high quality hardwoods that they can't use and will give away or sell cheap.
Look for a local sawmill - even amateur ones. They can be very inexpensive. One near me sells seasoned walnut for $2/bd-ft.
If you want a bit of challenge, discarded wood pallets can be a good source for thin oak. 1/4" or 3/8" (6 to 10 mm) thick is ideal for fretwork, and if it's a little twisted, stained, or has nail holes then it can add to the final product.
Some people like to scroll cut acrylic (plexiglass, Lexan, polycarbonate, etc.). It takes a little different technique to keep it from welding back together as you cut, but it can make some really nice looking projects.
Have fun. This is a great hobby.
