It's hard to pick one best in this category, but I've based this choice on the fact that Freud is the number one choice of most carpenters and cabinet shops. The familiar orange bits are found all over the place, especially in the commercial suppliers that professionals frequent. This set contains 13 of the most common styles of router bits, all with a 1/2 inch shank.
Manufactured with Freud's proprietary carbide formula for long life, all these bits feature a non-stick coating to reduce pitch build up and resist heat. The case can be hung on the wall or mounted on the workbench for convenience. Freud is so confident in their product that they offer a limited lifetime warranty.
CMT is a blade and bit specialist and this 13 piece set is similar to the Freud Super Router Bit Set, with a similar assortment of profiles available. Like Freud, CMT uses a proprietary carbide alloy with chromium added for extra long life. Anti-kickback features have been designed into the bits where appropriate and for those bits requiring a bearing for use with a template have them already built-in, cancelling the need to change bearings between bits for use. The set itself comes in a nice hardwood case.
You've probably never heard of Whiteside, but they have one of the most extensive lines of router bits on the market. This set has won the prestigious Fine Woodworking magazine's "Best Overall" and "Best Value" award for superior performance at an affordable price; that's a hard to beat combination. These are American made bits, which come with a lifetime warranty against defects in workmanship or materials. Made of superior carbide, they are precision round for proper balance at high RPMs. These quality bits will satisfy the needs of any woodworker but unfortunately they come in a plastic case, making them look lower quality than they are. The only reason I didn't put them as number one, is this set is smaller than the one offered by Freud.
If you're just getting started with routing, your biggest problem probably isn't which kit provides the best quality, but the one provides the most utility and getting the most for your money. That's where a kit like this one from Eagle America comes in.
Containing 70 sizes of router bits, this one will accommodate common routing tasks, including grooving and joining which aren't included in the smaller sets we've looked at. However, it doesn't have the large bits such as those needed for panel raising and building cabinet doors. The bits are carbide, all have a 1/2 inch shank, and come in a wall-hanging case. Eagle America offers a similar kit with 1/4 inch shank kits.
This kit probably provides the best selection for the money of any router bit set on the market. All 66 router bits are carbide tipped and have 1/2 inch shafts. MCLS produces a very similar set, their number 6083, which has the same bits in it but with a 1/4 inch shank for those that need it. Sizes go up to a 1-3/8" diameter ogee bit, providing a large variety in cutting. All bits which need bearings come equipped with them, saving you from having to change bits between setups. Packed in a nice display case which can be hung on the wall of your workshop, it's easy to keep these bits organized making this set an incredible bargain.