IMO ... I'd say don't mention the model search. Telling them about it will not enhance your chances with another agency. If an agency likes how you look and think that they can actually book you and make a commission from you, they will snap you up and get you going. And, yes, do go to as many agency open calls as you can ... this is the best way to get noticed by the actual bookers who work for agencies.
If you have a book ... and it's professional (from another agency), it's OK to show them. But if it is something you did on your own ... don't bother ... it won't impress them at all. The are interested in what you really look like ... just natural. So, they would be interested in having you bring a few snap shots of yourself ... against a plain background, in good light (outdoors, in light shade, no flash is best) ... and since you are a guy, do one with your shirt off or at least just a sleeveless tank top. Put your name, your stats (height, chest, waist, pant length, shoe size) and your contact information on the back of each. If they are interested they will take these for their files. And they might take a few polaroids on their own. If they do that ... you have got a chance with them.
However, if there is a delay, then they are not that interested. And if you don't hear back from them within about a week ... it's a "no", most likely.
Be very, very careful ... don't pay an "agency" or any "scout" any money up front ... it's not done that way. You don't need lessons or a web site.
If you get signed (actually sign a contract that lets them represent you) by an agency they will direct you to get professional photos done ... but only after they sign you. Then, they will send you to a good testing photographer (testing means taking photos for your portfolio), who knows exactly what kind of pictures they want. You will probably have to pay the photographer ... but never pay an agency directly ... that's a red flag that they might be a scam.
Agencies are supposed to make their money on commission ... you pay them (well, they collect the money from the client then take their commsission and any expenses you owe, out of that) only when you get paid for a job that they found for you ... period.