Does anyone have any particular recommendations on which one is better? I don't mind paying for iExplorer, I'm just wondering if there is any issue with reliability/safety/security with either of these two.

iFunbox is great, free, and works on both OS X and Windows.

Highly recommend it, it's what I personally use.

Also - note that this build of Gridlee is equivalent with MAME 0.139u1 - so when looking for ROMs, you may need to lookup the ROM on http://www.mamedb.com/ to see what version of MAME compatibility for your ROM/game was introduced (especially for newer arcade games).

I'm a newbie to this stuff and used iFunbox using the tutorial here:

http://www.idownloadblog.com/2013/01/27/mame-gridlee-guide/

The only tricky part that's missing from those instructions is that you have to run the game once before the roms folder is created.