Ok 1st off cut springs just suck! Why dont you just do it your self and save like 300 bucks, It stupid simple to do and ask anyone and they should be able to guide you through it. From what I have read (I have owned like 3 civics and put coil overs on many peoples civics and integras are pretty close) is that you have to get the shock forks for the front shocks. and the rears use 94-00 integra/ 91-00 civic shocks cause there alittle shorter and alittle fatter then the Da integra shocks. But if you want cheap but good shocks get the NAPA sensatrack, there good and get the job done and about 62 bucks each there alot cheaper. A good coil over kit would be Drop zone coilovers there 89 bucks for the kit and pretty forward to install. I have used Dropzone on pretty much an application ( DD, Drag, Road racing) and there a pretty good and I have never had a problem with them.
You're not quite on point. You only need the DC/EG forks if you're doing the DC/ DA hybrid suspension, which I strongly advise against. The height of the front and rear shocks differs on the DA and the DC/EG chassis.
Also, if you want to lower the car, do not but Sensatrack shocks. They are not intended for a lowered vehicle and will ride like crap and blow out in quick fashion.
OP, A decent set up is a set of Koni shocks and a Ground Control coilover sleeve. Better than that would be something like a Function Form Type 1 coilover, then a Tein Basic damper, from there you move into even better set ups like the Tein SS, K&W full coilovers, Progress Suspension coilovers, etc.
There are a lot of threads on here to read to get an idea of what set up is right for your needs and budget.