Beyond that simple advice, make sure it's a helmet for climbing. Cycling helmets have too many holesa jagged rock could easily sneak through one and leave a nasty gash or worse.
But which helmet? Petzl's Ecrin Roc ($84; www.petzl.com) is a fine, classic helmetsturdy, easily adjustable, and reasonably well ventilated. Fully approved for climbing and tested against a number of impact and shock-absorption factors. Petzl's Elios ($60) is another nice simple, reliable option, with its sibling the Elios Vizion adding a clear face visor designed to keep snow and ice off your nose when ice climbing. But that's a lot more than you need for the types of climbing you mention. Edelrid's Ultralight ($50; www.edelrid.de) is very similar in design and fit, and is considered by many a tried-and-true brain bucket. Lastly, the Kong Scarab ($159; www.kong.it) is certified for many sportsclimbing, bicycling, even whitewater kayaking. But it compromises in all three areas, and for about the same money you can buy purpose-built helmets for each sport.
So there you go. Climb on!
For more great rock-rat duds, including a sweep of essential starter gear, check out Outside Online's all-new Climbing Gear Buying Guide.