do I have to heed any Batfe regs for storing or transporting small quantities for use hunting or shooting at the range
Its State by State . You need the local regulations in your area regarding this, ATF only provides the federal guide lines. Like in Ma. here you need an FID to transport any amount, this includes going from point a to point b in your possesion this is the State calling for Fed ID for this pupose. You will find many states are not as stringent as Ma. - although even in Ma. you can posses BP and BP arms in your home (including pistols) with no FID, and can transport long arms with no BP loads without FID or local permit, but they require the FID and local permit for BP pistol and powder transport.
In Florida, it is most likely way more lax, but just call local police station, they will tell you what you need to do.