Any one of Konami’s Rebirth series are solid, WiiWare exclusive choices. I’ve bought them myself based on numerous reviews and a lot of research, but haven’t played them yet.
It consists of Castlevania Rebirth, Contra Rebirth, and Gradius Rebirth. I’ve heard Contra’s the best.
There’s also an exclusive Excitebike game on it.
There’s also the two Lost Winds games, but you can only get one, and the first ends on a cliffhanger. They were technically ported to iOS, but they don’t work on it anymore and were delisted years ago. It’s an open world 2D platformer where you use the pointer to create winds to get you around. It’s really cool. XD
I know a bunch of WiiWare games had demos. NyxQuest is one of them. It has a similar gimmick to Lost Winds, I believe (it’s been awhile since I played it) except its level-based. It had a Steam port, but it was really a game developed for Wii.
And Yet it Moves is also like that, on Steam but built for the Wii’s motion controller first and foremost, so its best played on it. It’s a really fun, creative platformer that has you shifting the whole level as you move through it. I THINK that has a demo too, and I’m pretty sure it’s also 1000 wii points.
Finally, there’s two games that are 500 points each that are just...weird, but haven’t bought yet. Tomena Sanner is one I heard great things about. It’s basically an auto runner where you need to press the A button to get through obstacles. Muscle March wasn’t so well received, but I’m getting it because it’s just a weird looking game. You play a muscled individual chasing after someone who stole their protein powder. You need to pose with the Wiimote and nunchuck to get through holes in the wall.
Hoped that helped. If you want something more in-depth, both Antdude and Scott the Woz have fairly good videos looking at games in the Wiiware library. Aside from Musclemarch, these recommendations are based on those videos, among other reviews.