My advice fwiw, ONLY book flights direct with the airline.
The reason is simple. Booking through an agent, you are a customer of that agent not the airline. So when it all goes to shit, you'll be dealing with the agent not the airline. By booking direct you are the customer of the airline and their obligations reflect this.
If you miss a connection or something else happens it could just be the difference between buying a new ticket or not.
Other things that get screwed up between the agent and the airline are things like seat choices or meal requests. Much easier to sort direct, but alot harder via an agent.
Personally speaking I fly just as often with easyJet as I do BA.
If you want to add accommodation and car hire/transfers most airlines will offer to add these to a booking, but they're just as easily sources elsewhere... Although the above applies just as to the extras. If you can book direct and be very clear about your itinerary.
Also, just because you can book a 45 minute connection, it most definitely doesn't mean you should. There are several very good reasons to allow at least 4 hours.