Good question re: matching sailboat to lake size.
The most frequent/convenient lake I sail is about the size of yours. While I'd love having a larger lake - it is close and I often sail several times a week, after work, whenever the wind picks up. You can have a lot of fun when the wind is at 90 degrees to the 1 mile length.. those are decent runs, when its not, you'll get lots of practice tacking. Either way - at least you are out sailing!
I've had a Bravo, Wave, AI's, and a H16. I never used the H16 on the small lake - way too much boat. The Bravo was a LOT of fun, but in my mind - a one person boat. If you are going to sail alone most of time- you might think about the Bravo. It seemed to be more responsive in light winds and well suited to the smaller lake. I sold it and got a Wave - which on larger lakes I really appreciate, and when I take the wife, dog, buddy, whatever.
Either way - get a boat - to have a lake across the street, and not go sailing seems criminal.
'08 Hobie Wave, Hobie Adventure Islands