some questions on my e36 suspension

hello. let me start off by confirming if i'm correct that shocks and struts do NOT lower the car's ride height whatsoever. right?? ok that's one and two is my e36 is my daily driver. but i do plan on an occasional autocross and i love to take nice drives. SO. do you guys recommend a spring and shock/strut combo or go all out n get the coils? (btw trying to keep away from the pricey side because i would really like a nice ride height compared to paying a lot more extra money just to have the car handle so much better than it would with getting the shortest suspension setup). anyways, so i just want to know if there is a cheap set of decent coilovers that drop the car a lot and improve handling that i should get or a decent spring and schock/strut combo that will give the car a real nice drop and improve handling. i would appreciate if you guys could throw your opinions and some examples at me but just keep it cheap and affordable!! thanks in advance

p.s. shocks and struts. same thing right?? different name? thnx