Should I use lead free solder?

Use leaded solder if you can. It is easier to work with, requires lower temperatures, and there are less quality issues with the joints. The only reason to use lead-free solder is if it is not allowed in your jurisdiction or you are want to sell soldered goods someplace (like Europe) where this is forbidden for practical purposes.

No, lead in solder doesn't pose more of a health risk to you when soldering. The vapor pressure of lead is so low that there just aren't significant numbers of lead molecules in the air as a result of soldering. The predominant health danger from soldering is inhaling the vaporized flux. This is made more dangerous by lead-free solder since the temperature required for a good joint is higher. Even that is a small issue compared to different types of fluxes. If you are worried about this, use a fume extractor. In any case, avoid breathing the immediate vapors from soldering, whether leaded or lead-free and regardless of the type of flux.

Lead free solder can be really hard to work with.

If you buy a name brand solder, which isn't 99%Sn and 1%Cu then it will be similar to leaded. Personally I use 95%Sn 4%Ag and 1%Cu. You will need a bit higher temperature on your iron. I have a Hakko FX888-D and I use 310C° for lead free and 265 C° for leaded.

Lead free alloys will eat away your tip a bit faster, and you will need to clean the tip more often (oxide forms much faster on the solder on the tip). At first I hesitated to switch, my first'experience was with a cheapa$$ soldering iron (directly to mains one) and cheap "Lead Free" solder. Lead free solder is a bit more expensive (I payed like 14€ for 100 g of lead free solder, diameter 0,5 mm, stannol brand).