I'd recommend a directional outdoor wireless bridge. Keep the frequencies down to get a bit of non-line-of-sight performance. Since you mention barn and greenhouse with a fair bit of distance I assume we aren't talking an urban area here, so hopefully not a lot of interference. I have a few very similar setups here in our rural area (I do wireless problem solving, among a few other things, for a living).
At that range a set of 3 Ubiquiti LocoM2 radios (~$50 each), one at the house as AP and one each at barn and greenhouse as SU's (Subscriber Units, Clients, etc) should get the job done as long as you can see around the barn. The Loco has a relatively wide (about 60 degree) beam so the ends don't have to be in line. The LocoM2 has a range of about 2 miles at multi-megabit speeds. If you do your own installs you should end up well under your budget. Engenious and Mikrotik are others that have similar equipment.
If you aren't comfortable drilling holes, running wires, or crimping Ethernet connectors you can get it installed professionally or find someone local that can get the work done for a pizza and six pack (actually, I've quite happily accepted fresh chickens, freezer beef, venison, elk, and salmon, both smoked and fresh, among others - There are benefits to knowing how to terminate a cable). If the barn and greenhouse are in line I'd try the direct shot first, but you may have to add one radio and hop house to barn and barn to greenhouse. Configuring the radios is through a web based GUI and not much harder than most home routers.
When folks ask why you need broadband to the barn, by the way, the best answers I've gotten so far are "So the Cows can watch Mooooovies" and, with a client that put cameras in the lambing pens linked to their living room TV so they didn't have to constantly go out to the barn to check status, for EweTube.