This is always an entertaining topic. All the calibres mentioned would be fine. Other "typical" (whatever that means) calibres to consider would be:

.308 - a good all -around cal for all N America big game excluding Alaska-Yukon conditions

.303 Brit (if in Canada) easily available, and affordable, good all-around calibre

7mm08, Another decent all around up to elk - marginal for moose, mild recoil

25-06 Probably best limited to deer/varmits, nice flat shooting cal if longer ranges are expected

.243/6mm, A good youth gun - Definitely limited to deer & varmits (has been used on elk and will work if you know what you're doing - the rest of us should get something heavier) usually considered the minimum big game calibre, very low recoil.

.223, other centrefire .22 cal - They'll work , but may not be legal. A good way to start an argument if they are.

First thing to do is check the laws where you want to hunt. A lot of states have minimum caliber rules for deer and you wouldn't want to buy a gun for hunting that turns out to be illegal to use for hunting! That said, I can't imagine that any state would consider a .270 or larger too small for deer. Still, check your laws before you lay out your money--and do NOT trust what some salesman at a gun shop tells you! In my experience, 3/4ths of them haven't got the first clue about hunting regulations.

Next question, what kind of hunting do you expect to do? If you're going to be still hunting through thick woods then a .30-30 lever action will work fine. If you expect to take 250 yard shots from a treestand, across a 160 acre bean field, then a .30-30 would be completely inappropriate.

Finally, the short answer to your last question is, none. With optics you pretty much get what you pay for and if you want decent optics you need to budget almost as much for your scope as you do for your gun. The scopes out there that go for less than $100 are, frankly, cheap. They will work, but only just. There is no point spending good money on a nice, accurate rifle and then putting a barely-adequate scope on it. Plan on spending AT LEAST $200 for a decent scope--a really good scope will be $300-$400.

If you go to your gun shop and look at the ammo you will probably see the majority of ammo with a .270, 30-30, 308, or 30-06 sticker on it. There is a reason for that. They just plain work! The 30-30 is limited in range so I would lean more toward the other three.
The mossberg should be a no-nonsense rigid hunting rifle which is all we even need. I am not one to buy the prettiest rifle just to look at. It is a tool for me and needs to work.
As for an inexpensive scope, it is true what denver said that you get what you pay for but we have all been there before and when funds are tight you try to get the most you can afford. Bushnell sells some decent scopes in that price range. My father just buys the low end bushnells and they have never left him down. His is riding on a .308 pump so recoil is not really an issue. I get about 5 more minutes of viewing time per day with my Leupold over his scope so there is not that much difference. That being said, I would not put that scope (his bushnell) on my 300RUM and expect it to stay together.

If your going to be hunting in wide open places, I'd go with the 270, 30-06, or 308, assuming we are talking about deer. If your hunting elk, I'd go with the 30-06 only. If you going to be hunting forests and brush, I'd go for the 30-30 (quick, short range shots, possibly w/ iron-sights).

Bushnell and Simmons make scopes in your price range. You might want to visit some local gun stores, chances are good you may be able to pick up a decent used rifle with scope. Also Weatherby, Savage, and Remington all offer new scoped rifle packages.

Where do you hunt? Selecting a rifle/cartridge combination is a very subjective matter. Frankly, all modern calibers are good and most deer won't know the difference between them. But, bullet selection is important. I've seen many deer taken and using the 30-06 as an example, time and again, deer drop more quickly to the 150 grain loading than to the ever popular 180 grain loading, a bullet a bit too strongly constructed for whitetails.

I happen to like short action rifles. The Remington Model 7 in 7mm-08 is jst about perfection as a whitetail rifle. it's short and handy enough to use in the woods yet can reach out 300 yards when necessary. Ammo is inexpensive, recoil and muzzle blast are mild.

No one can say anuthing bad about the .30-06 or the .270, two all time greats. regarding the .270, you would enjoy reading the late Jack O'Connor.

A 243, 25-06, or a 260 Remington would be very good choices, not to mention the 7mm-08 and 308.

The hot cartridge is the 270 WSM in the Win 70.

Go with the .270. You said your dad has a 30.06 so it would be useless to buy one. A .270 can do just about the same as an 06 just a little bit quicker.

As far as scopes. I purchased a simmons 3-9x50 for a bout $60 becuase that was what i could afford at the time. I havent had any problems yet.

Happy Hunting.

I am not going to enter into the calibre argument, but befor eyou pruchase the mossburge, look at the Weatherby Vanguard. Probably the most affordable rifle on the market now. As to optics, you get what you pay for.

If you are on a budget you can pick up a Savage scoped package for under $400. They are very very accurate and have an excellent trigger. The finish and stock are a little on the cheap side but you are on a budget right? As far as caliber 30-06 is probably one of the best all around calibers out there. Lots of bullet choices and it is probably the most used hunting catrige ever. You can pick any cartridge to death but the 06 is as good for any an everthing as you'll find. I would'nt even consider a 30-30 just because even if you hunt cover and want a brush gun you may find yourself waling back to the truck sometime and see a great buck 300 yrds out across a wheat field and say crap I wish I would have bought an 06. Just get a low power scope that will give you a wide field of view.

On optics its true you get what you pay for but if you want an opinion I think you can find some good optics for around $100. Try a simmons they are'nt too bad. But For about $110 you can get a sightron S1 in 3x9 that's a suprisingly good quality scope. On ebay there is someone selling burris 3x9 fullfield 2's for $150 with ballistic plex reticle. I personally think that is the best buy in optics right now a fantastic scope that won't break the bank.