Most deer aren't huge,but they do have different sizes depending on area of country and available food,that and Mule Deer are different than Whitetail. Hunting terrain does matter in rifle and cartridge selection. If you are hunting in the western US or Canada, or out in the Plains, you could be looking at shots well beyond 30-30 effective range (125-150 yards). The 30-30 is considered a close in "brush gun", but I personally have never been a fan: it is a very limiting and anemic low power cartridge that was great for 1898,but the 7 x 57 Mauser created a paradigm shift (good phrase to look up). If I were to get a lever action, I would get a Browning BLR or used Savage Model 99 in a modern cartridge like 7mm-08,308,30-06 or something similar.
I don't see the advantages of a lever action over a bolt action anyway, you should always concentrate on making the first (and only) shot count. Bolt actions give you the best value for the money, provide ease of use and cleaning,accuracy and dependability. There are some rifles I can't recommend like the Remington 770/710/715, but it is hard to find a bad choice in a modern rifle.
As for cartridge/caliber, I bought my first 30-06 when I was 14 and had no issues with recoil, and I've had one ever since. My 12 year old can shoot reduced recoil ammo in it, but he is physically not quite big enough to be comfortable shooting it with full loads (5ft and 100 Lbs). He can use a 243 very effectively,but I handload for the rifles and we're using a premium bullet with very specific restrictions on bullet placement and range. 243 isn't the best caliber for the novice hunter because it lacks bullet mass;not energy-has plenty of that. The 243 uses the same "short action" case as a 7mm-08 and 308, and I suggest the 7mm-08 over 243. My son puts 3 boxes of ammo on target when we go shooting,so I have no problem with his ability,I bought the rifle as a coyote gun to begin with and he likes it-but it is a limited use rifle for deer right now.
308 is going to recoil more than a 7mm-08,just laws of physics at work there,but it isn't a bad recoil.
Long action cartridges like the 25-06,270,280 and 30-06 are all based on the 30-06 case. Any would be great for most deer hunting, and like the 7mm-08 and 308, would also serve as elk and bear rifles (the 25-06 would be a VERY marginal choice for those however).
If you live in an area where you have multiple hunting opportunities then you need to adjust to the larger animal-since I hunt deer and elk I use 30-06,deer only would be 270 as an example.
I have some links for cartridge/game matching, and comparative effectiveness of calibers,along with some representative rifles to look at.
As for buying a rifle, you can look at it multiple ways, get an "Entry Level" rifle or combo package for $500 or less(some less than $400) but the scopes are going to be economy scopes you will need to upgrade later, or you can buy a rifle with a real value over $500 and then get a scope for it-and expect it to not only give you years of enjoyment,but your children too. That is an investment decision to discuss with your folks, but I would rather spend $490 at Cabela's for a Weatherby Stainless Vanguard or $600 for a Savage "Weather Warrior" that will last decades than a $320 770 Remington that has ZERO resale value and might not last 5 years without problems. They do make "youth rifles" that can either adjust to your arm reach as you grow, or come with two stocks. Depending on your size you may or may not need that.