I shall certainly send them a copy of *The Sign of the Cross*
To paraphrase something Uncle Jim is fond of saying: don't start at the bottom and hope for the best; start at the top and work your way down. If you feel you need an agent, then focus on that exclusively. If you try and find a publisher while you're agent-hunting, then every rejection from a publisher is a closed door for your prospective agent. Do one or do the other. Don't do both.
If you do choose to go the publisher first route, start with the very best: Random House, Simon and Schuster, St. Martin's, etc. Small presses and e-pubs should be approached only
after the larger houses have passed. But, if by some chance a larger house is interested (and most don't accept unagented submissions), then that interest will allow you to bypass all the query business and get an agent quickly -- you need only ask the interested editor if s/he knows the name of a good agent you can talk to. Generally, such an "in" won't be possible with a small house.
Like a small business, you should have a plan in mind for how you're going to grow (something a bit more concrete than "sell my book"). Do you want to start small and work your way up? Then you're going to need to approach the more influential small houses; you're going to need your book to be physically available on book shelves where the consumer can see it. You're going to need a small house with enough cachet to get you a review in places like
Publishers Weekly or
Library Journal. Write well, sell well, and the larger houses will take note.
On the flip side, do you want to shoot for the pinnacle? Start out with the big boys? For that, you're going to need an agent with clout -- preferably one that apprenticed with a larger agency or who "jumped the desk" from the editorial department of a large press. They must have the contacts to get your work read by top editors, and the skills to negotiate the highest possible advance. Remember, this is a business whose central theme is the acquisition of properties that generate sales. A bit of a mercenary mindset is required at that level.
That's my advice
Good luck to you!
Scott