Iris recognition is the easiest and most reliable; the reason it's less popular is it was wildly overpriced until the patents on the technology expired a few years ago, but since then a number of players have entered the market and you can actually play with free software that will perform iris recognition via a Webcam, which might be all you need. Retinal scanning feels extremely invasive to users; you generally need people to put their forehead up against a rest and hold still and users typically won't accept it outside of an extremely sensitive environment. In contrast iris scans can be performed from several feet away, very quickly, and generally work through glasses and contacts. Iris recognition typically also works well with people who have a number of different diseases (like diabetes, which can dramatically affect retinal patterns over a very short timeframe) or conditions that affect the eye, unlike retinal scanning, including most of the common conditions that cause blindness (except cataracts). Fingerprint recognition has gotten a bad rap because in general use people don't want to have any false negatives, so operators tune the environment to be less sensitive, leading to lots of false positives (my fingerprints get read as your fingerprints). But it's true that prints can be affected by things like dehydration and the local environment; they can also be simulated if you're sufficiently motivated, but that's made infinitely more difficult if you combine your biometric with a PIN (though it can't be argued that prints are left lying around everywhere, so it's probably not the best biometric you could choose). In addition a surprisingly large number of people -- like maybe two percent -- simply do not have usable fingerprints; it's actually a diagnostic criteria for some medical conditions. (I have actually had a couple of jobs that dealt directly with use of biometrics as a form of authentication).
In general I think the other comments are on the money: Keypad and PIN sounds like the way to go. If you're trying to create something automated, then contactless cards / dongles are the other solution but as others have noted, this isn't bulletproof since without some other factor (something you know or something you are) it's possible for one person to use somebody else's device.