Endless Space is a very fun strategy game, and I believe there is a demo for that (can't tell because I own it
). It is also cheaper than some of the 'kings' of strategy, while being better (imo).
Otherwise, my suggestion as someone who has been on there 7.5 years, is make a wishlist by doing searches of game styles you like and checking the meta score, reviews, and descriptions. With a wishlist, you can also have Steam send you an e-mail when it goes on sale, so you can save money. Keep an eye on the featured games too, because you may find something for cheap that is also fun (like FTL: Faster Than Light, which is currently half-off at 5 bucks).