The ideal router for dovetailing is a fixed base type with a good depth lock. It can either have a 1/4 or 1/2" collet, but the 1/2" dovetail bits will flex less and do a little bit better job, but 1/4" bits will work. If you work in metric, a router with an 8mm collet is the preferred size, or you can adapt 8mm dovetail bits to fit a 1/2" collet using one of the collet bushings that are sold for this. The router does not have to be very powerful. A smaller, lighter router of about 1 hp is adequate for dovetailing. Your arms will thank you for the light weight router after cutting dovetails for several hours.
For most dovetail jigs your router should be capable of using guide bushings and these bushings will need to be well centered to the collet. I've had the best luck with the Porter Cable style bushings, but these aren't required if your router uses a different style bushing that is non flexible and can be perfectly centered around the router collet. Some routers require an adapter to use the Porter Cable type bushings and there are bushing sets being sold that include this adapter, or it can be purchased from the router manufacturer. Another option is to replace the router base plate with one that has a counter bored 1 3/16" center hole to allow the Porter Cable bushings to be used.
With either style bushing you should use a centering jig to be certain that the bushing is centered to the router collet. These centering jigs are nothing more than a precision ground shaft that fits your router collet, with a cone shaped piece that slides snugly on this shaft. To use it you place the shaft in the router collet and tighten the collet, then slide the cone down on the shaft until the small end touches the router bushing. You then loosen the bushing and press the cone against it to force the bushing into the center. Then re-tighten the router bushing. You then remove the shaft and cone and replace it with the dovetail bit.
There are some dovetail jigs that use router bits with bearings attached. These do not require bushings to be used on the router, since the bearing on the bit rides against the fingers of the jig to guide the router. Since no router bushing is used, no centering steps are needed. The Katie jig is one of these.