Yes, RF will work.
You'll need the remote and base station.
$200 is a bit low in budget. URC's MX-850 and an MRF-250 base station can be gotten as a bundle from
www.surfremote.com for around $275. You can also get the Harmony 890 for the same price.
If you don't want PC programmibility, you may be able to get an MX-600 and basestation for under $200. However, lack of PC programmibility usually means lack of discretes, which means tricky and sometimes not functional macros.
If you're looking for a less complex line of remotes, I guess you can do it. Check out the RF20 from URC and the MRF-100B basestation--that retails for under $150.