I have the following two tables in my database (the indexing is not complete as it will be based on which engine I use):
Table 1:
In MySQL 5.1 later, you should use InnoDB. In MySQL 5.1, you should enable the InnoDB plugin. In MySQL 5.5, the InnoDB plugin is enabled by default so just use it.
The advice years ago was that MyISAM was faster in many scenarios. But that is no longer true if you use a current version of MySQL.
There may be some exotic corner cases where MyISAM performs marginally better for certain workloads (e.g. table-scans, or high-volume INSERT-only work), but the default choice should be InnoDB unless you can prove you have a case that MyISAM does better.
Advantages of InnoDB besides the support for transactions and foreign keys that is usually mentioned include:
See also my answer to MyISAM versus InnoDB