My parents & I went to Beijing 2yrs ago. We went to both places you mentioned and a couple of other places - Tiannemen Sq, Temple of Heaven, and Forbidden City.
We just went to the concierege at our hotel and booked the tours through them - we knew it was reputable. There were bus tours (which we did) and more private 1-on-1 tours.
Although we stayed at the Grand Hyatt Beijing, we had people on our tours from Marriott and other hotel chains.
I just used this guy - john ping - to go to the great wall on New Years day 2010 . I phoned him with 1 hour notice and he managed to juggle something to come take us. (my bad planning!).
He speaks fluent english had a reasonable car ( a few years old buick ) and charged a reasonable rate. 600rmb for trip to great wall at mutyianyu gave me advice on the place etc. Chatted with the kids in the car teaching them a bit about china. I wouldnt call him a Tour Guide but you dont really need a tour guide at the great wall - you need to get there and walk around it and feel safe that someone will be waiting to take you back and get you there safely. When we went it was -10 and snowing! He gave us advice on the route on the wall etc (left hard - right easy ) where the tobbogan was etc. . In contrast - a taxi to do the same thing (without guarantee of seatbelts and no english spoken)was about 400rmb for half-day hire, and the Marriott Audi a6 with driver was 1,800 rmb. The journey is 45-90minutes each way depen on traffic.
his website is http://www.beijingcardriver.com/
He will take you to places to eat - en route if you want and do a custom day tour etc. Very trustworthy in my experience with him for the day and what Ive read about him on tripadvisor
We booked a tour with a Concierge 1 day before our actual tour during the coldest season in Beijing. Despite the wetaher and short notice, they were able to book the tour for us. We availed of the "bus/van tour". But because of the freezing temp, me and my 2 other colleauges were the only one in the van. Hence, it appeared to be somewhat "private tour". Tour guide name is Kelly (i forgot her last name) although she had problems speaking in straight English, she spoke better English than other Beijing locals. She was fun and nice too. Took pictures of us and my colleuagues. She did not gave her contact information though. But you can ask the concierge to look for Kelly if you wish. Tour package was 570RMB only (Great Wall, Forbidden City, Dr Tea house, Silk house, Jade Museum and Traditional Medicine Research center). Price is inexpensive and reasonable.
I can refer you to a very good guide in beijing : Lily Yuan. She can provide very good history and speaks excellent English. She can also arrange a car to take you to the Great Wall. I have used her several times and also have recommended her to friends.
Her e-mail address is: email@example.com