Which MySQL storage engine is the most similar to ARCHIVE when that is not available?
InnoDB supports compression as of MySQL 5.1 (with InnoDB Plugin), or natively in MySQL 5.5. The level of compression really depends on your table content, but I see 75% reduction in size as common.

Reads and writes to compressed tables involve more CPU. InnoDB will support your foreign keys as well as any indexes. 

I would say it is a fairly good out-of-the-box solution for your problem.

MyISAM only supports compression on a read-only mode. 

Or you might find an altogether NoSQL solution to do the job well for you, given that you don't really need indexes.

I'm a relational geek, so I would first go for InnoDB. Just:

ALTER TABLE my_table ENGINE=InnoDB ROW_FORMAT=COMPRESSED KEY_BLOCK_SIZE=4;


KEY_BLOCK_SIZE can be 1,4,8,16; Lower numbers will give you better compression. My experience shows that 4 gives good compression. 1 rarely improves much, and consumes a lot more CPU.