As far as power goes not much depends on that as far as a receiver. It's the transmitter doing all of the work, power wise. But as mentioned the antenna's design can dictate range, along with other things such as how high you mount it or if there's any pre amp, which I suppose would use a bit of extra power. Suppose a good tuner MAY use more power than a less good one but probably negligible.
For a solar setup I would look at a car radio as it's already made to run on 12v and it will have a decent tuner. Easy to find 12v stuff as far as solar goes. Small charge controllers, batteries, etc. I would try to aim for like 30w solar though, 6w is kinda low, as you won't always get that rating. That rating is pretty much perfect conditions.