AVCHD will allow you to record in 1080p, but MP4 will allow you to put more video on the card (at a lower (but close) quality level, however at 720p). I have a 64GB card and I can record about 6 hours in AVCHD MXP mode (highest bitrate = highest quality within MP4 or AVCHD). Whether you can tell the difference between MXP and FXP is up to you. If you are burning to blu-ray, playing on the computer, or playing from the computer to a 1080p TV, I would say AVCHD MXP mode if you have the capacity. If you are burning to DVD (not blu-ray) or displaying on an old tv or 720p set, either AVCHD MXP/FXP or MP4 9Mbps will likely be so close you won't notice.
There is no internal memory, so you have to use a separate memory card (SDXC, SDHC, SD). The HC and XC are "High Capacity" and "eXtreme Capacity" and allow for a greater number of GB. The chart in the product description is accurate on the recording time at different quality levels and memory card capacities.
Also, the best way to get the videos/images after recording is to use the memory card slot on your mac to transfer since the basic Mac software is better than the package that is included with the video camera.
It is according to how you plan on playback. If you plan on watching the video only on your MAC, then record in MP4. It is also easier to upload or share in this format. But you will miss out on viewing your video in full HD mode if watching from your TV. In my best opinion - record in both. If you are shooting a video to share with family/friends, etc. then choose MP4. But, for instance, if you are traveling and shooting the video to document each event, then by all means record in AVCHD. I use this camcorder for travels to Europe (Holland, Germany, France & Austria). I documented in full HD format. But I also carried 2 spare batteries and 2 spare removable memory cards at all times.
I actually bought the camera for my fiancé. And he records On a removable sd memory card. i bought him a 16gb memory card and hes recorded a lot and still has a lot of memory left. The quality is great.