Probably the best way to start is to post up links to the boats that you are considering - the combined expertise on the site here will/might give you an idea if a boat is worth persuing.
Have a look at it, preferably with a knowledgeable friend, and come back to us with any questions you might have.
If it looks like the boat for you You'll need to think about how much additional inspection you need/want.
Having an outboard engineer inspect the engine will be money well spent. Even though i'm a Surveyor when I bought my boat I had an Optimax experienced engineer inspect the engine.
Finally the rest of the boat can be inspected. This is what I can do if you need it. The inspection that we do isn't really rocket science, most of it is visual - to look for cracks etc, some of it is hammer sounding to detect delamination or separation of structures, some of it is using a moisture meter to detect water in the transom or deck, some of it is simply switching everything on to see that it all works.
Once the boat has been inspected we'll draw up a report detailing what we did and what we found and will assist in dealing with any defects that are discovered. All boats have some defects, some serious, most not serious.
Whether you need me to do this, or do it yourself or have one of the very knowledgeable other members on here come along and look at the boat only you can decide.
Regarding "buying from a reputable Broker" we need to make the distinction between Broker and Dealer.
A dealer will own the boat and will be bound by the sale of goods act giving you some protection. Similar to a car dealer. They will have an interest in selling you a good boat so there's no comeback - but also some may be interested in selling you tarted up rubbish!
A broker will be selling on behalf of an individual and in effect he is simply assisting in a private sale. You have no protection. This is similar to dealing with an estate agent.
The diligence that individual brokers may or may not take when inspecting a boat they are selling or advertising varies - but even the most diligent of brokers (such as Dry Run and others) can be caught out by something that they weren't aware of or didn't spot. (Remember all boats have defects and dealing with the defects is where the deal either goes forward or dies!)
I hope these ramblings are of use and feel free to ask away!
Thanks for the recommendations Jim, Kieron and Ian