edit

First of all you should get the albums those songs are off of:

She Smiled Sweetly - Between the Buttons (UK or US, I think it doesn't really matter on this one. UK is easier to find though since UK is higher than US on the order list)
I Am Waiting - Aftermath: UK (Better cover art, more songs)
Dead Flowers - Sticky Fingers (Part of the their 5 best albums)
2000 Man - Their Satanic Majesties Request (Most people consider it to be one of their worst ABKCO-era albums. But if you can get into the faux-psychedelia, this album is a keeper!)
Girl With... - Some Girls (Another part of the top 5 albums)

After you get those albums make sure to get the remainder of the top 5:
Exile on Main St. (Their best and bluesy-ist album)
Beggar's Banquet (Great album, not too many "singles" songs, just good rock)
Let It Bleed (Incredible. Remember, "THIS RECORD IS MEANT TO BE PLAYED LOUD!")

And that will give you all the must-haves!

Get Exile.

Everything but their 80's & early 90's albums. A good way to start would be to pick up all of the SACD hybrid reissues. Throw in Exile On Main St. Some Girls, and Sticky Fingers, and you'll have a great RS experience for days and days.

Exile yourself.

My fave Stones albums are Let It Bleed, Sticky Fingers, Goats Head Soup, Some Girls, and Voodoo Lounge.

Let It Bleed. Super, super album.

Exile on Main Street
Let it Bleed
Beggar's Banquet
Sticky Fingers
Aftermath

Some great - if lesser known - Stones tunes:

Emotional Rescue
Star Star
Loving Cup
Rocks Off
Just My Imagination
Before They Make Me Run
Connection
Moon Is Up
Country Honk

I'm not even a Stones fan, but Exile is quite possibly the greatest rock record ever recorded - but only as a whole - the songs don't reach the same heights when taken out of the context of the record. The album is far greater than the sum of it's songs.

But you have to let it grow on you - it took me a few years to recognize it's greatness.

That's a great selection of Stones songs you've got there. They're some of my favorites as well.

Get Hot Rocks 2: Fazed Cookies. It's got a lot of the stranger early Stones stuff.

Definitely get Between the Buttons, one of the best albums they ever released and completely different than most of their other stuff. Aftermath is another fantastic album from a little earlier.

I can't recommend 12 X 5 enough, which is a fantastic collection of very earl Stones blues covers and such.

The classsics: Exile, Let it Bleed, Beggers Banquet, can't go wrong with them, but they're more blues based rock (classic Stones sound) than the stuff you cited. get them anyway.

If you've got the scratch, spring for "The London Years" boxset (is it still in print?) as it contains all of their a sides and b sides from their classic period. Like a lot of British bands, the Stones released a lot of their best stuff as singles rather than on albums. The London Years is a great, comprehensive (and easy) way to get all of that stuff.

I second that you pick up the London Years. It's a 3 CD set containing the Stones eariler hits alongs with some B-side it also comes with a nice booklet with a little background on the group along with all the lyrics of the music. It still available on Amazon for about $60 but you can proberly find it cheaper in someplace. Recommend.

For some reason I can't ever get tired of this song. My favorite Richards song, even more than Happy.

Here is some of the best Stones Songs ever recorded, and they aren't very well known.

She's a Rainbow
She's So Cold
Jigsaw Puzzle
Ventilator Blues
Child of the Moon
You Got the Silver
Saint of Me

Don't be scared to pick up Bridges to Babylon, its a new album that didn't get the chance it deserved.

My absolute favorite Stones song is Jumpin' Jack Flash. Unfortunately it's not on any of their studio albums though. As for early Stones, I also recommend Out of Our Heads. I know many purists may disagree, but I kinda prefer the US versions just because they include most of the singles.

That's why you buy a hits collection from that time (Green Grass or Past Darkly) or the Singles Collection.

But, to be quite honest, the ABKCO years of The Rolling Stones' carreer is such a meandering hodgepodge of US and UK releases, singles and one-offs that there really is no "correct" version of anything. Allen Klein is a greedy dirtybag and managed them for sheer monetary value.