Hi,
The 4921 is only as an example of a medium power transistor, there will be thousands of others that may be more apt for your circuit. At a guess, I'd suggest using a BJT rated for 3 Amps continuous current, with as low a VBE as you can find (that isn't stupidly expensive), and read the datasheet specifications, at least look for the graph called "Safe Operating Area" to check it can actually handle 0.5A at 5V continuously, even if it's described as "3 Amps continuous current" in the description.
There's usually a "Digikey" link here on EDA, it'll have a super parametric search tool to locate the right transistor quickly, it's always good to compare a few datasheets, even if it takes a little time, to select what's right for the circuit you are building.
I'm sorry, I am unfamiliar with your circuit in several ways, so it would be inadvisable to attempt to provide a schematic for you. Whatever you do, if the webpage you are following for the design is reputable/sensible/seems to have tested the circuit themself/etc, if you don't follow the instructions properly it's unlikely to work.
The 2N2222A, whether plastic or the metal capped version, which I like capriciously, is a little transistor that isn't really suited to operating at half an Amp at all, the TIP35 is a high power device meant for much larger currents which you don't need, so: "not too hot, not too cold, but just right" would presumably mean a medium power transistor, that's the difference in my opinion.
If it works with the TIP35, then fine, seems OTT. Hope you have a DMM, as important as the circuit. If you ran out of insulated wire, don't you have any old broken electronic or household device you might be able to salvage some similar wire from?