1. Your first gun should NOT be a semi-auto. The accutrigger on that Savage is about 100x better than a 10/22 trigger. Good triggers go a LONG way towards a rifle's accuracy. A bolt action is inherently more accurate than a semi, especially with a Savage bolt compared to a 10/22. A bolt action is WAY, WAY easier to clean.
http://www.vortexcanada.net/products/riflescopes/crossfire2/crossfire2_4-12x40ao_bdc.html
Plenty of good scopes in that power range show-up used on the EE too, you should be able to get something really decent for about $150. New Crossfire IIs are all under $300 though if memory serves.
3. I like heavy barrels on .22s, but they're really meant for shooting off a rest. A bench (like at a shooting range), a bipod, shooting sticks, etc. Offhand shots are not easy, and not comfortable. That said, it's mostly what I use...and I make due. If 75% of your shooting will involve carrying it on long hikes, offhand shots, get a standard-weight barrel. If you like the heavy barrels, you should REALLY consider this model;
I love Savages, love the Accutrigger, but those plastic stocks they put on their guns are garbage. NOT simply the cheap feeling or aesthetics, rather, the geometry. They only work if the gun they come with has iron sights and you plan on using them. When optics are involved, your cheek (=eye) is going to be too low. That laminated stock version is way better, and for the extra $100, you get a nicer feeling gun, metal trigger guard, recoil pad and (not that you'll need it) higher resale value.
Back to the 10/22~I used to own one, and like you...I got tempted by the red dot. Didn't like the gun, didn't like the red dot. (bought both new) Semis are fun, but I don't ever suggest them as a first gun. When the time comes for one (after you have lots of mileage on a bolt gun) do yourself a favor and look at Marlins. Until then, get yourself a Savage...a 1/2-decent scope, lots of different ammo to try, and enjoy watching the bullets go exactly where you point the gun.