Nothing is really great about the 501-504 flashlight apart from they are good for the cheap price. Being cheap doesn't mean they are bad though.
The beam will depend on the emitter, generally a XM-L will be the brightest but not always (depending on the driver)
For $10-15 you wont get batteries and a charger for that, never buy the cheapest charger and batteries. You will need about $20-22 for a reasonable charger and batteries if you choose to go for something that takes 18650 batteries.
For the money ($15 limit), this is the one frequently recommended light that stays high on my wish list and it doesn't need special batteries, charger, etc. It also has a nice slim profile for EDC. The R5 has a nice throw to use the available lumens, which are very reasonable for the AA power source. It is probably where I would start given your original post.
If you stretch to $23 for a package with charger and l-ion battery you could move into 18650 territory, I like the Sunray S-R5 with XML package I got off AliExpress. It uses the same P60 drop-ins as the 501 etc family and is very comfortable to hold. My own sample of this didn't run on high with the supplied battery, but the seller resolved it to my satisfaction.
The XML puts out a lot of floody light with some good throw. The XML center isn't really much brighter to the eyes than the R5, but the spill is a lot brighter. So far, I haven't been convinced there is a good flood to zoom option for the XML. I suggest looking at a lot of beamshots to see which style of beam you like.
If you are stretching to spend the $15 I'd make sure you have a seller with a good reputation who will stand by you if there are problems with the light. I'm also not a fan of 3*AAA lights but many others are, and they offer a quick backup option.
If you want to go for less money, the Sipik lights seem to have a good following but I can't recommend a sample or ebay seller.
For another package deal, this looks like a good $20 package deal from the same seller I got the SunRay from. The C8 does a pretty good job of giving some throw from the XML, but it uses a different "pill" instead of the P60 drop-in. If you like the larger head size, this light gives a great beam. My son has one and it competes pretty well with my 53mm Trustfire.
18650 are not dangerous per se as long as you're monitoring charging/discharging with a DMM. Repeated overdischarge makes them prone to vent with flame (eg catch fire/explode) if you're unlucky. It does not happen very often -compared to the wide use of these cells there are very few reported incidents- but when it happens it gets very nasty.
If you happen to be near Strängnäs you could drop by and take a look at some lights I have lying around. Although I wouldn't consider myself primarily a flashaholic I have enough leftover parts that I could build you a flashlight or drop-in for a few beers (or cokes if that's your preference).
