Your route depends on what you want to see. We have taken all three routes and the road through Seeley Lake is definitely the most scenic. The town really is crowded in summer and parking can be a problem. But, if you like narrow, hilly streets, 19th-century buildings, good restaurants, unique shops, and maybe even a weekend craft fair, it can be a fun small-town stop. And you can always stay in an RV park and use the toad to tour the historic part of town.
Missoula to Flathead Lake and Kalispell is the long way around and not as scenic as Hwy 83. Missoula is a small city (70,000) and Kalispell is a big town (20,000) and both have lots of traffic. You would be able to stop and see Butte if you go all the way to Missoula.
The easiest route, if you are not real comfortable driving on winding mountain roads, is through Helena and north on US 89. Helena is the same size as Missoula, but you will be on I-15 through town if you come north on US 12/287, so in-town traffic isn't really a problem. If you don't need to stop, you can be through Helena in 15 minutes. It is the state capital, however, so it is worth a stop or maybe even an overnight. Unlike Missoula and Kalispell, Helena started as a mining camp, so is more interesting if you like museums, historic buildings, and gold rush/mining history.
Have a great trip!