Best Linux filesystem to use on MMC memory chip?
If your filesystem is read-only, use ext2. That is proven stable for several decades, is fast, efficient, supports ownership, supports permission bits and has a huge user base as every Linux box supports it. In other words it supports everything a decent Linux system requires.

If read-only is not an option, your next best bet is ext3. Apart from all the properties that ext2 comes with, ext3 brings journaling.  This means that every change on disk is only committed once it has actually been written to disk. Very stable, proven technology. A problem with ext3 is wear leveling.

Ext4 improves on performance in several use cases, but comes with more CPU overhead. Most distributions today default to ext4. Apparently it reduces unnecessary writes, which is good for an SSD. Ext4 has a TRIM extension.

Next in line it BTRFS. Don't go there. Although several distributions offer BTRFS or even default to it, it wasn't stable last time I tested it (H2 2012). You don't want to use a filesystem that hasn't proven itself under stress. Too many bugs are being fixed.

Linux offers a wealth of filesystems, but the ones I mentioned above are the most common ones.

Of course there is FAT32 (vfat), don't go there. It is old, it suffers from fragmentation and doesn't allow for ownership and file permissions.

NTFS is closed source, don't even think about it. Yes it kinda works on Linux but the implementation is fully based on reverse engineering (because Microsoft doesn't release any technical details) and the Linux implementation is just not reliable.

A JFFS2 needs to be entirely scanned on a mount, so mount time increases linearly with device size. This is caused by the fact that there is not some sort of tree structure to store files.