Dewdrop, I always book holidays and flights online, so the very best of luck if you decide to do so. I do a good bit of research beforehand, on sites such as Tripadvisor.com, in order to find what accommodation is best, what sights to see etc. Yes, you can book directly with hotels, in my experience. On Tripadvisor, you will also find links to booking sites and it enables you to compare prices etc. I dont honestly know how much of a saving I make, versus booking through a Travel Agent because I have done this now for many years. You need to think also about things like the transfer from the airport to your hotel. Again, on the travel websites you will find lots of useful information on this.
Just one thing, there is no value that can be placed on your peace of mind, knowing that your Travel Agent has booked everything for you, might be worth the price difference. I dont know, but it's just a thought.
As I said, very best of luck and I wish you many happy years travelling.