Hi. I'm a fan of receivers because you can generally get a better deal for your money, due to how popular receivers are. However, I'm not sure how much you'll need to spend to get video conversion (i.e. component to HDMI) in a receiver. I'm guessing in the >$300 range, but I don't really know.
You can buy switch boxes that will let you connect one HDMI input and one component input with one HDMI output, like you mentioned, such as
this one for about $60 before shipping.
You can also get a converter for component to HDMI like
this one and combine that with an HDMI switch like
this one (there are several kinds available). Those two would run you about $65 before shipping.