Never, Ever Use Originals.
When compiling your portfolio, each piece should be a copy of the original artwork, not the artwork itself. Copies can be resized to fit your portfolio; copies are also replacable, while the originals are not. If you lose your portfolio, that can be recreated. If you lose your original artwork, you've lost something much more valuable that you've put a lot of time, effort, and thought into.
Always Use High-Quality Prints.
Original artwork should be scanned at at least 300 DPI, though 600 DPI is preferable for color. After being resized to fit the portfolio size that you've chosen (I usually prefer an 11" x 14"; it's large enough to display pieces well, but easily carried), you should take them to a professional printing service (most would recommend Kinko's, though I've had various bad experiences at the local installments of that particular chain) and print them out on clean, smooth, high-quality paper. You can go with paper as thick as cardstock, if you'd like, to keep the pieces from bending and creasing and to attain better paper quality; however, I wouldn't recommend glossy paper, because they'll already be behind a gloss of clear, protective sheeting and that will just double the glare.
Running your portfolio off on your home printer from shabby, low-resolution scans is never a good idea; you end up with grainy pictures on low-quality paper, and most home printers can't handle larger-size paper to fit in standard portfolios.
Don't Settle for Shoddy Binding to Save Money.
The portfolio itself is as much a part of the presentation as the pieces inside it; if you want to look professional, spend a few extra dollars to buy a nicer case in leather, vinyl, or even pleather, as long as it looks well-made and neat. Skimping and buying the plastic, velcro-tabbed portfolios will add an amateurish feel to your portfolio, and will detract from the quality of your work; what that says to potential employers is that you're not willing to invest in presenting yourself nicely, and people viewing your portfolio will probably spend more time eyeing the scratched and bent edges of the plastic box than your artwork.
Plastic was fine for quick high-school presentations. It's not acceptable when you're preparing the results of your educational labor in order to enter the work force. Unless you absolutely can't spare another penny, spend the extra money. It'll be worth it.
Don't Ever Leave Your Portfolio With Anyone.
By the time that you finish, you may have poured hundreds of dollars into the creation of this presentation piece. While it is replaceable, do you really want to? Your portfolio should enter with you, and leave with you; however, there's no harm in having smaller samples ready to leave for further perusal.