When you say you are looking for improvements in handling, do you mean less body lean in cornering? Is your context one of general, occasionally spirited, driving? Autocrossing, more competitive events?
My experience is only with my Tiger, but I think some of it is relevant to your Alpine as well.
Are you generally okay with how the car rides in a straight line and over bumps that affect both front wheels but do not like the degree of body lean in turns? If so I highly recommend a thicker anti sway bar and urethane bushings. Addco makes one (7/8 inch diameter vs stock 3/4 inch). I have seen them from time to time for $99.00+ shipping on ebay although more recently some guy was wanting $199! I got one several years ago for my Tiger and was really pleased with the cornering improvement. I have since gone to a 1 inch bar and reinforced arm mounts and really like it even more. Note that the straight ahead ride and handling is not affected by the anti-sway bar (unless only one wheel deflects of course).
While the difference between 3/4 diameter and 7/8 diameter may not seem like much, the stiffness goes up by the square of the radius (or something like that). You will note a significant difference between stock 3/4 and aftermarket 7/8. Also, the urethane bushings control deflection better than the stock ones, which is also going to help.
Speaking of bushings, just replacing your current, possibly well aged rubber bushings with new ones will probably give you a surprisingly noticeable improvement in your handling. Maybe you would just want to give that a try first. I know Sunbeam Specialties sells stock replacement rubber ones. They may also have stock sized urethane ones. Just be sure and use the proper grease on them during installation if you go for that version.
Shocks and springs really need to be discussed in combination since they should be designed to work together. I have upgraded both on my Tiger, but think what I have done there is less relevant to your interests. I have also lowered my car front and back, but I am guessing that is something beyond what you are interested in doing.
Hope at least some of that is helpful.
Gene