I'm fairly new to planes and have a Goldberg Eagle 2
The CG Eagle 2 is still one of the best trainers out there....period. After 35+ years of flying RC planes, I still keep an Eagle 2 ARF around simply because it's a joy to fly. Plus an Eagle 2 is capable of performing some fairly advanced aerobatics simply by adjusting the balance point and the control surface throws.
The engine is an old OS 4 stroke .65......
Are you sure it's an OS .65 4-stroke? I've been flying RC planes since 1969 and don't remember OS ever making a .65 four stroke. The only OS four stroke sizes I can remember are the .20, .26, .30, .40, .48, .52, .60, .61, .70, .75, .80, .90, .91, 1.20, 1.60, 2.40, and 3.00. Could it be one of these instead? Or maybe a different brand? (For example, Saito makes a .65 four stroke.)
....the front right mount is broken. My dad thinks it will be fine to run it as is but I disagree.
I agree with your Dad. Just make sure to keep an eye on the right rear mounting bolt to make sure it always stays tight.
....one of my worries is that the engine is to big for the airframe.
An old .65 four stroke will definitely be at the upper engine weight limit for an Eagle 2 to fly well. But an old .65 four stroke definitely won't be too much power for an Eagle 2. A modern .52 four stroke will probably have equal power, and a modern .46 two stroke will be more powerful. (My Eagle 2 ARF currently has an OS .46 FX.) Besides, that old four stroke has a throttle to control the amount of power.
HOWEVER.....if this is your very first attempt at flying an RC plane, I'd highly recommend putting that old four stroke back in storage and getting a different engine for your Eagle 2. There's no sense in risking damaging that old four stroke during the training process.
If we should get another engine, what do you think we should go with? Reliablity, longevity, and a decent amount of power.
Around here the most popular engines for training with an Eagle 2 are the Thunder Tiger Pro .46, the OS .46LA, the Thunder Tiger .42GP, and the OS .46 FX(AX). All of these engines run extremely well, have excellent throttling characteristics, will idle reliably at very low RPMs, and will instantly accelerate back to full power without hesitation. Any engine with those four qualities will make the training process much more enjoyable for both you, and your instructor.