Yeah, at your size a shorter rifle would probably be best. The 7mm-08 is a great deer round for anyone so would not hesitate to use it. The 7mm-08 is based on the .308 Winchester and the 25-06 is based on the 30-06. By 'based on' I mean that they have the same shell casing and the round it is based on. Both the .308 and 30-06 are 30 caliber and shoot a bullet that is .308" in diameter. Since the 30-06 has a longer case, it hold more powder and therefor shoots a bullet of the same size faster. So, given a .308 and a 30-06, the 30-06 will shoot it faster and therefore deliver more energy to the target but both is plenty for deer to somewhere around 400 yards or so.
That's just some background to help you understand how the 7mm-08 and 25-06 compare and relates. The 25-06 uses the same case as the 30-06 with a smaller, .25 caliber bullet (.257" diameter I believe). With the larger case, the 25.06 shoots a smaller bullet at a higher velocity. Many consider it the best Antelope rifle because the high velocity means that it shoots a very flat trajectory. With the long ranges the typically come with antelope that is a good thing. Also, antelope are smaller animals the so the smaller bullet is just fine here. I used to have a hunting buddy that used this round on whitetails and he liked it just fine.
The 7mm-08 uses te same case as the .308 and again with a smaller bullet. A 7mm bullet has a diameter of .284". So, it has has a larger bullet that the 25-06 but with a smaller case that holds less powder so it does not have velocities as high as that of the 25-06. However, it is still a highly affective deer round. I have heard some people state they feel that 7mm-08 is perhaps the ideal whitetail round. I'd say you could make arguements in this regard for several different rounds and all would probably be valid. But, I doubt you would find any folks who know what they are talking about that would tell you the 7mm-08 is not a fine load for deer. And FWIW many Elk have been taken with them as well.
I like the 7mm-08 because it comes in rifles with a short action. I think that would be good for you because in addition to a shorter stock , the shorter action would result in a rifle that is again bit shorter than say a 25-06. I am 5'11" and I would enjoy that as it would make the rifle a little handier, especially if you spend any time walking through dense brush.
So in my opinion, and that's all this is, I think a youth gun in 7mm-08 would be just great for you. Just not sure if you can find a left-handed youth rifle without quite a bit. So, maybe you look for a standard sized one with a wood stock and cut an inch off the stock.
Also, one last peice of advise. When making this sort of decision understand that for the most part all, or at least most, of the options you have to choose from are great. Any of the traditional deer calibers in a rifle from any of the traditional manufactures will be a great choice. So, with that being the case, I would recommend you choose the one that for whatever reason appeals to you the most. And don't feel like you have to justify it beyond that. If you see a Savage in 7mm-08 that really turns your crank, go for it. Or if it is some other caliber from some other company go with that. If the rifle excites you and adds to the enjoyment of the hunt, that is the one you should choose.