There's no doubt that the Intel compiler is a excellent. It's just rare to hear from a student who is looking for that much power. For the lightweight code most students write, the GNU compiler is more than sufficient. You are very well informed and ahead of most of your peers.
The Visual C++ Express edition doesn't really play a role if you want to use SlickEdit and the Intel compiler. To do development, you need the following components:
1) Editor -- in this case, SlickEdit
2) Compiler -- in this case, Intel
3) Debugger -- again, should be part of the Intel package
4) Build system -- with SlickEdit, you have two choices: a) use SlickEdit's build system or b) use an external build system.
To use the Intel compiler with SlickEdit, you should use the "Other C/C++" project type. Select Project > New and expand the "C/C++" node to find it. You will have to configure the builds, yourself. Once you have created a project, select Project > Project Properties and then select the Build tab. That's where you can set which build system to use.
I haven't configured SlickEdit to work with the Intel compiler. In most cases, it's very straightforward. In Project Properties, you select the Tools tab and then configure the Compile, Build, and Link tools. You enter the command line to perform each of those tasks.
If you use an external build system, like make, then you just have to invoke make when you want to do a build. If you use a standard make system, SlickEdit can read the make files and add build targets from the files.