Big Sun light-readable screen
You must be able to see the display in varying light conditions from bright sun to shadows. This is more problematic with color displays. Displays with fewer colors have less layers in their displays allowing for more light to pass thru to reflect a brighter display.
The larger the display, the more map area you can show at the same zoom level making it easier to coordinate with your surroundings. In any event, I use a screen protector on mine to keep the displays from getting scratched.
A mapping GPS is not a requirement for GeoBiking. It does make it nicer for mapping trips though. I don't know of any recent color GPS that doesn't do maps. Non-Mapping B/W units may actually have an advantage over their mapping counterparts in reduced clutter (Tracklogs are then the main "map" features.) I've missed trail connections on B/W mapping units because the trails just didn't stick out from the map.
Color displays make it much easier to assimilate information quicker. This really helps to allow quick glances enroute. On color units, you can change the color of the tracklogs to help make them stick out from the background data.
Tracklogs are a GeoBiking requirement if you can't load one of my map versions. Most newer devices support 200 tracklogs at one time and some can support "drag & drop". My network is over that size now, but not all has to be loaded at one time.
Touch screen GPS are easy for most people to operate. I'm sort of a hold out in that respect when it comes to bicycle mounted devices though. I can operate a button controlled GPS much easier while pedalling.
Memory requirements are determined by the type & quantity of maps you want to use. Having a memory card slot allows you to add pre-programmed map cards such as the great Hunting GPS Maps. I like aerial imagery on my GPS, but don't use it as much while pedalling because it takes more time to "read". Imagery (and raster maps like USGS quads) eat up a lot of imagery
Ease of Data Entry
Ease of data entry on GPS is not that important when using supplied maps/tracks etc as when you are you are creating them. To me it is very helpful to be able to enter data quickly in the field. To that end, a touch screen device is quicker, however, I do fairly well entering data on my DeLorme PN series. (Correcting mistakes, adding spaces and changing case is aided on those devices with some one key shortcuts.).
Dedicated Cycling Features
Garmin makes some dedicated cycling GPS devices (Edge Series). They are great for fitness/racing aspects of cycling. I don't use them because I'm not a racer, and regular GPS have better tracklog features.
Most modern GPS have reasonable processor speed for GeoBiking use. Scrolling of imagery or raster maps can be slow to respond when looking outside your immediate area on some devices. The DeLorme PN 40 &60 scroll better because of dual processors, and the Garmin Montana series also appears to be quicker than their other handhelds.