The radiation emitted by Uranium ore is generally low & the samples are safe to handle.
Some ores emit substantially more radiation than others (Torbernite & Pitchblende for example), but the samples are still safe to handle & inspect. Even though the radiation produced by these samples is reasonably low, continuous exposure to the higher level samples is certainly not recommended.

   Radiation damage is cumulative, and although picking up a high level sample to inspect it is no cause for concern,  putting a chunk under your pillow and sleeping with it night after night for months at a time is something you should avoid. It's not a teddy bear.
In case a small chip, crystals or powder comes off of your sample while inspecting it, it's a good idea to wash your hands after doing so.

   Ingesting radioactive material is something we recommended you avoid no matter how good it may taste to you. As with many things, a little common sense goes a long way, and with a couple simple precautions, these materials are quite safe to deal with.

   For those that like to hunt & collect their own Uranium & other Radioactive ores, take close note of the following:
The ~gigantic~ quantity of deep underground Uranium ore found around Uranium mines & deposits produces Radon gas and many other radioactive elements as part of its natural decay process (see chart below).
Radon is a heavy, odorless, invisible, radioactive gas.

   Having several small Uranium samples in your room isn't a factor for concern, but those of you that collect tens or hundreds of pounds of the stuff, need to be aware of potential Radon levels. Take a hundred pounds of Uranium ore, put it in a room, and in a few days you'll find that the Radon levels have risen to dangerous levels. Radon gas decays into a radioactive metal, and if there is any Radon in your lung at the time it decays, it will transform into a metal particle, and sit forever in your lung emitting radiation that your cells won't be all that happy about.

   If you just find it necessary to own giant piles of radioactive ore, keep it outside. If you must store it inside, invest in a digital Radon detector. It will continuously display the Radon levels and should they ever rise too high, an alarm goes off. It's a worthwhile investment for the serious collector.

   Let me state again that several small samples even the size of your fist are no cause for Radon concern... it's the large collections we're talking about.
Of course if you'd just keep them in a zip-loc bag, or out of the house entirely, Radon gas would be nothing to be concerned about no matter how much of the stuff you've got. Also keep in mind that if you go exploring abandon Uranium mines, there is a substantial amount of Radon gas waiting in there for you.
Radon is a very heavy gas that sinks to the lowest level quickly. Functioning Uranium mines have giant ventilation systems that replace the air several times an hour and those abandon mines you have so much fun collecting in, have nothing but stagnant PURE Radon Gas... sometimes at 100,000 times "safe" levels.

   Breathing in a pure Radon gas atmosphere is not a smart thing to do. You can't stick a mask on your face and filter it out, so don't bother.

   Just stay safe and don't go into any abandon Uranium mines... there's plenty of samples to collect in the tailings piles outside of the mine to keep you busy. Or even better yet, let us take the risk and simply purchase a sample from us.