You can use a rake of sorts to move the brass. The problem with using a broom is the fibers of the broom each act like a thousand small brooms, stirring the debris in the air. The less the debris is stirred, the better. You can also use a brass picker, like one of those reach things they advertise on TV for us old people to reach stuff out of normal reach. They really do work great for picking up brass, and eliminate all that bending down, but you only pick up one or two pieces at a time. With practice, you get pretty good at using it, and you can reach that elusive brass that fell just in front of the firing line, without actually putting body parts out there.
The biggest problem is the constant accumulation of contamination that indoor ranges incur. It's just something that goes with shooting indoors, but a lot of ranges aren't willing to mitigate it. They tend to treat their indoor ranges like outdoor ranges, which naturally have more air flow and disseminate the contaminates better. Outdoor ranges still shouldn't have carpets, etc. at the shooting positions, since they're pretty much contaminant magnets. Likewise, it's not prudent to eat or smoke while shooting, until you've washed your hands to remove the contaminants that you have on your hands. It's no big deal really, but just practice good hygiene and you'll be ok.
It's not necessary to dress up in a HazMat suit to handle brass, or to reload. You just have to know that elemental lead, i.e.; solid lead, isn't absorbed through the skin. Only vaporized and oxidized lead is absorbed by inhaling or ingesting, so you want to get those contaminants off your skin before it comes in contact with your mouth or nose. If it makes you feel better, you can wear a dust mask, but it's really not that necessary, as long as you're careful about the other handling issues. Some people wear rubber gloves when reloading, but that's not necessary, either. If it makes them feel good, then I won't tell them not to. I wear latex gloves when sorting buckets of brass that I buy from our club, but that's only because my hands get black from handling all that brass, and I can just peel the gloves off when I'm done with a bucket and a simple wash of my hands takes care of the dirt, etc. When I don't wear the gloves, it takes orange hand cleaner with pumice to get them clean, and several washings. It's just a matter of convenience to me.
You can handle the brass as you normally would, but wash your hands afterwards.
I'd suggest any shooter have their lead levels checked whenever they have an annual physical. If nothing else, it will ease your mind if you're concerned about it, and the blood levels are in the lower range. On the other hand, if your blood levels are high, you can take steps to remove the lead from your blood. One of my shooting buddies finally had his lead level checked and found out it was 61, which is way high, and is reportable to the state health department. He didn't like getting that phone call, and his wife didn't like it even more. He hadn't been taking any precautions, and never washed his hands after shooting, or handling lead. I suggested he take large doses of Vitamin C, which he did, and got his level back down in the normal range in less than a year. Oregon considers anything under 19 as "normal", but it varies by state. I like for mine to be below 10, and the last time I was checked it was at 9. Keep in mind that I cast bullets by the many thousands on both my Master Caster and commercial casting machine, so I have a lot of lead exposure, even before I shoot a round, which I do a lot of, too. I also have a bullet fragment in my body that's been there for a long time, but it can't be absorbed in it's solid state, so my doctor said to just ignore it, which I do.
I'm a fanatic about washing after touching lead, lead contaminated materials or shooting, and it pays off.
I hope I've answered your questions, but if not, keep asking and I'll try.
Fred