As Scary said many of the mid-and high-end devices currently on the market have wireless charging capability built-in although you have to buy additional accessories to make it functional. But depending on your definition of "cheap" devices it may be a while before it trickles down to that end of the market.
You might be able to purchase a second-hand device that has it for a reasonable price, depending on where you are located. In the US the best reliable source for used Androids is Swappa. And there's Ebay of course but you have to be careful to verify the seller's reputation.
Solar charging is not something that is likely to be built into any devices as the panel size required for a useful charging rate is way too large. A panel that fits on the back of your phone would require it to be left out in full sunlight for a full day or more to get a complete charge, not very practical. There are aftermarket solar chargers you can purchase that have large fold-out panels capable of giving a decent charging rate in bright daylight and have a standard USB port you can plug your phone or other devices into.