Which to use: innoDB, mySQL or a mix?

I am beginning to program an interactive web site with a database which I will have hosted remotely in a shared server. I will need transaction-safe support either by using transaction-safe tables such as innoDB or BDB, or by using myISAM with table locking in my PHP code.

From the many inquiries that I have emailed to Web hosts, it seems the vast majority offer only myISAM and other non-transaction-safe tables, and say they have no plans to offer innoDB or BDB.

Does anyone know the real reason? One host said innoDB and BDB are not good enough yet, but I do not get that impression from anywhere else on the Web; certainly not from the mySQL or innoDB home sites themselves.

Also, elsewhere I keep finding comments that innoDB and DBD are for large sites only, whether or not the site needs transaction-safe support. Yet the mySQL and innoDB manuals seems to indicate that the real difference is that they are transaction-safe, rather than that myISAM is more limited as to the size it will support well.

Do any of you know which is so, or is it both.

If you know a host that offers innoDB, please tell me their URL or email address.

TIA,
Will