I think you've nailed it. If not, start another thread next week. 🙂 You will need an ethernet NIC for the machine hooked up by wire to the router, but those are cheap if you don't already have one.
Even though it might be a little more expensive, I might be tempted to get a separate router and WAP, but a combo unit such as you describe is probably fine too. The key thing is that, with a separate WAP, you may have more flexiblity with placement, plus a separate WAP may have a few more bells and whistles with it that may eventually come in handy. Also, a modular setup gives you more flexibility if one part breaks down or if you want to switch to some new and improved technology in a few years. But, if you are getting a strong signal with your current setup, a combo router/WAP is probably fine. Good luck.
Even though it might be a little more expensive, I might be tempted to get a separate router and WAP, but a combo unit such as you describe is probably fine too. The key thing is that, with a separate WAP, you may have more flexiblity with placement, plus a separate WAP may have a few more bells and whistles with it that may eventually come in handy. Also, a modular setup gives you more flexibility if one part breaks down or if you want to switch to some new and improved technology in a few years. But, if you are getting a strong signal with your current setup, a combo router/WAP is probably fine. Good luck.