Is it normal to stop so much because of thighs burning? I've taken up cycling because of an operation I had in August 2015. My consultant made it clear I had to get regular exercise. 

I thought cycling was probably one of the best exercises I could do. 

I'm finding it so hard on hills, even a gentle uphill slope. 
Very painful butt and aching, burning thighs. 
The butt I can live with. But the combination of both stops me from wanting to go out. 

My last ride was 17 miles. And 24 two days before. Combination of all gradients. 
Not far into my ride, I hit a gentle uphill climb and my thighs started burning. I tried to ignore it but had to stop for a minute then go again. 

It seemed I was resting longer than I was cycling. Probably about 10 revolutions. It seemed ridiculous.
I'll be 57 in two days time. 

Is it because I'm new to cycling, and my age? 
Maybe I'm doing too much? Is it normal and does it get better with practice?
More than likely it is normal and frankly your legs probably aren't used to it. 17 miles is a long way for a beginner so I would pat yourself on the back for that.

You may also benefit from a proper fit from a bike shop. As a lot of beginners either have their seat too high or too low which can limit your power and actually cause you to tire quicker, although a fit takes a lot more into consideration that just that. Either way it would probably be worthwhile to at least look up a good guide and check your posture, it can make a big difference.

Regarding your age, I am 32, and know several people in their 60's that could leave me behind going up hill (or anywhere) with ease. 

I am in okay shape, and have been riding off and on for several years and still have to stop from time to time. It does get better though.

You may also take a look at your diet and pre-ride foods, it is also important that if you are going on a long ride you take some snacks for along the way so that your body has some fuel to burn. Eating 30 minutes to 1 hour before a ride vs not eating at all can make a monumental difference. 

Bottom line you have made a healthy choice and a fun one to improve your own health and way of life! Keep at it and don't give up or feel bad if you need to stop and catch your breath from time to time, the most important thing is you are out riding!