The problem with any mini-amp is that it isn’t going to have much power.  
I’d just get something full-sized (used if your budget is tight), put it in the house, and run the speaker wire.  It’s a casual-listening situation with low-fi speakers, so the typical reasons for not running speaker wire that far don’t apply.  
The best wire to use is probably the stuff they use for outdoor low-voltage lighting, which is rated for direct burial.  It looks like common lamp cord, only black.  Sixteen-gauge is fine, but you can go with 14 ga. if your worried.
Regards,
Wayne A. Pflughaupt