usually the cheapest hand chuck is quite a bit better than the cheap key chuck those HF drill presses. They will get just as tight as you need them to be. NO KEY TO MISPLACE. They are very quick and easy to use. Highly recommended. Enco has them on sale often. Those HF drill presses use a Jacobs 33 or JT-33 chuck - NOT a J-3. (you should verify this first - it could have changed but I doubt it) You can find a hand chuck on sale for $25 to $30 all the time.
It may be a HUGE surprise to many, (it was to me) that the only thing holding a Jacobs type drill chuck in place is a tapered cone shaped shaft that fits into a socket on the chuck and just the friction holds it in place. (some industrial drill presses have locking shaft chucks)
To remove a chuck, you use a drift key and tap it between the top of the chuck and the drill press frame. The drift key is a wedge shape. I don't have one so I just use a big screwdriver. Place a rag on top of the press table so when the chuck comes loose and drops, it land on the rag.