If you're going to do any compilation, install the build-essential package. This pulls in GCC, make and other basic development tools.
I recommend using kernels packaged for Debian. If you compile your own, you'll have to get the configuration right, and to install it properly. Getting the configuration right is difficult, as there are many options; you'll probably forget an essential component the first time, and it can be difficult to figure out what's missing. Furthermore Debian sets up its system with an initramfs; if you go with an initramfs, you'll have to regenerate it with the modules you've compiled, which Debian's setup scripts do automatically. If you don't use an initramfs, you'll have to make sure that all the necessary drivers are in the main kernel image and not in a module. You'll also need to make sure to register your new kernel with your bootloader correctly.
Debian provides the kernel-package program to build a kernel the Debian way. Use it. In addition to pulling in all the dependencies you were missing, it'll take care of packaging the kernel properly.