I've never owned a Mega ST, so some of this is from memory of things read in the past and from talking with friends who do.
The Mega ST was the same as the regular ST for the most part except that it came in a pizza-box configuration with the keyboard plugged in separately, similar to the style that was increasingly popular in the late 80s. It does include a cartridge port, which is important here as the NetUSB device Fletch mentioned requires it.
As mentioned above, there was also a later STE variation, also available in "Mega" form, for which they used the Atari TT case plastics albeit in a slightly different color. Again the keyboard plugged in separately. The Mega STE has space for an internal hard disk which is handy, and an expansion bus that pretty much no one uses.
MegaSTEs seem very rare, especially in North America, and so be willing to pay a premium if you really want one.
Note: There is no single ST that will run every software title without some issues.
Problems occur with different TOS versions - from V1.0 to V2.04. TOS 1.62 seems the most compatible with everything.
Also video modes. A lot of games require 50Hz "PAL" mode, although the latter STs can easily switch to this with a simple program in the AUTO folder.
Hard disk drivers can interfere with some picky games.
The STe/Mega STe had extra hardware for audio and visual. Few games every used it but there might be some games that simply won't run on a stock ST or Mega ST.
If you are adamant that you want the Mega version, look out for:
Is the keyboard included and does it look to be in okay condition?
Demand pictures of the battery bay. Many Mega's suffered from leaking batteries when their owners boxed them up and forgot to remove the AAs. Battery leakage can destroy a motherboard. Non Mega Atari STs did not have battery backed clocks.
And for all STs:
Look for proof the unit boots up to a desktop - not just a power LED. Fixing STs is a rare and special skill so unless you are good with scopes and soldering irons...
Is the unit from your country? STs were much more popular in Europe than North America, leading to many enthusiasts later importing Europrean units to the U.S. - that's fine but the composite signal is going to be PAL, not NTSC, and the power supply will be 220V.
Look for pictures from all angles. Many ST owners hacked their cases to accommodate Gotek drives, or turbo switches, or whatever, and most of them were not very skilled with a dremel.
Is the mouse included? The ST mouse is unlike the Amiga or PC, so you can't just swap them over, although they are still plentiful on Ebay.
Does it include a video cable? The Atari video plug is unique so you will need to buy or make a special cable for the Atari's 13-pin DIN video port.
To move files from your Mac to any ST:
NetUSB has already been mentioned, and is a good method - but you will also need somewhere for the transferred files to land. The Mega STE can house an internal hard disk but other STs, including the original Mega ST, could not. Look up the Ultra Satan as a SD-card based hard disk alternative that plugs into the ASCI port. The SD card can be removed and read on an OS that can handle FAT file systems, which I believe the Mac can. Then you can drag and drop your files.
ParCP is another option. Plug the adapter into the ST's parallel port and run a USB to your Mac. I can't remember if the software supports MacOS or not so you might end up having to run Windows or Linux in a VM. Then you can transfer files to the ST over the USB cable.
Overall I'd agree with Fletch. If you are just looking to get into some games consider a 1040STE. Easy to upgrade, can run most applications with little fuss and besides the daft mouse/joystick port location under the keyboard they are easy to live with.