CPUs with integrated graphics work just fine when you install a dedicated graphics card. AMD's APUs are just names for their CPUs with integrated graphics. Intel's CPUs almost all have integrated graphics, so there's no need for the distinction. If I were you, I wouldn't get an AMD APU. Instead I'd go for an Intel motherboard and CPU.
Since you're looking at an APU, I'm guessing you don't have the largest budget. You can get an i3-4130 for $125 (or $90 at Microcenter) or an i3-4150 for $130 (or $100 at Microcenter). Both are excellent, but the 4150 is a tad stronger. Ideally, you should try for an i5 like an i5-4590 for $200 (or $160 at Microcenter). All three of those have integrated graphics and are great performs and will perform much better than an FX CPU or an A10 APU, so if you haven't gotten a motherboard yet, I recommend getting one of those.
UPDATE: Once you get a dedicated GPU, there isn't much you have to do hardware wise. Very rarely, depending on your motherboard and other things, your computer might still use your integrated graphics instead of your dedicated card. If that happens, and it usually doesn't, you can usually manually switch between the graphics card on your desktop, or you can disable the integrated graphics all together in the BIOS.