You are making a good choice with the Bilstiens they are top quality. I don't know why you would consider changing just the rear springs. I replaced all 4 of mine because the fronts were sometimes bottoming out spirited city driving. I replaced the shocks at different times then the struts I used Boge which were OEM and KYB on the rear which I was not too happy with.
If there is a shimmy in the front check for loose tie rod ends,idler arm, ball joints etc but first check for a bent rim and go to a tire shop that balances the tires with a high tech machine that gets then exact espacially if you are spending big $$$ on Michelins.
1990 190E 2.6
1996 Grand Voyager 3.3
1985 Mustang GT 5.0 5 SPD
1982 Suzuki GS 750T