Definitely look into a permanent display shelf-- and make it big enough for all the Muppets that will follow now that you've taken your first plunge-- but also invest in some large ziploc-style plastic bags to keep each figure from rubbing against others when they're being stored. Rizzo will fit in a regular sandwich bag, the others might need the larger freezer bags.
As for what to get now, Bunsen really cries out for the Muppet Labs playset with exclusive Beaker figure. And the others are all sorta lower-tier characters. I'd say to start with, you need a Kermit, a Fozzie, a Piggy, and most definitely a Gonzo... he's a good one to either drive your Sam Eagle crazy or buddy up with your Rizzo.
Choose whichever versions you like best or can afford on your budget. Me, personally? I recommend the original naked Kermit, naked Fozzie, EB variant Piggy (or First Mate Piggy, exclusive to the Swinetrek playset, but then that will demand a Link and a Strangepork) and the purple-tux Gonzo with Camilla. He's the quintessential version of Gonzo, although he's gonna cost more than the daredevil Gonzo.
After that, you may want to pick single characters for a while. Scooter, Beau, Marvin Suggs, Lew Zealand, Newsman... guys who don't really necessitate the purchase of any other characters.
Because eventually, you will find yourself with a Floyd or an Animal, and that's when it becomes a real obsession... to own a 'complete' Electric Mayhem.
And then you'll get a character in a tux, and want all the others. These are the 'slippery slope' Palisades figures. Next thing you know you're careening down the list of completism.
Ah well, there's worse addictions in the world. Have fun!
Alex