Most Infrared receivers are actually 3-pin digital receiver modules that have internal circuitry to filter just a certain pulse frequency commonly used for TV remotes, and they just output an on or off signal, so we can't use them for measuring distance. We need plain analog IR photo-diodes or photo-transistors.

Looking at several low-cost IR photodiodes and phototransistors, I purchased a few that had good potential. Besides making sure the IR receiver has a peak of roughly 940nm to match the IR emitter as explained in "Choice of Infrared wavelength", ideally the IR receiver also has a daylight-filter so that visible light does not effect the results much. (I'm not sure whether the daylight-filter is of much use when using 940nm since the sun doesn't have much 940nm radiation, but it's worth having the daylight filter just in case!). Ideally the emitter & receiver are both fairly narrowly focused instead of too wide-angled. Comparing phototransistors vs photodiodes, phototransistors tend to be more sensitive & thus better, while photodiodes might be best with an extra transistor to boost sensitivity, but since I'm trying to minimize the components on the finger where the sensor will be, and putting the transistor a few inches away from the photodiode might introduce more signal noise, my preference is a cheap 940nm phototransistor that includes a daylight filter and has narrow focus.

Infrared receiver options at roughly 940nm wavelength (sorted by price for single-quantity):

If the receiver has a wide beam-angle, it's not such a big problem because we can easily fit a small black plastic tube around the receiver so it effectively has a small beam angle, therefore we can ignore the beam-angle column. All the wavelengths are quite close to 940nm, so we can ignore that column. I don't mind if it's a 3mm or SMD form-factor, but 3mm is easier to attach the plastic tube around, and 5mm is larger so less ideal. Daylight filter is nice, but might not be needed at 940nm. So the 3mm phototransistors have preference over the others. And since price is a big issue, the TEFT4300 seems like the best option since it's cheap, has a daylight filter, is a transistor, and is 3mm. The only downside of TEFT4300 is that its peak is at 925nm rather than 940nm, but since it's quite close there probably isn't much noticeable effect. So I'll use a TEFT4300 phototransistor as the receiver.