I understand you want to LEARN to shoot. Start with a 22 LR and a semi decent scope, if you want one. Read about, and UNDERSTAND how a bullet works. Once your groupings are getting better, move up to 100 yards. Your .22 rifle should be good for 100. Do not change your caliber (and I made sure to write "change", and not "upgrade) until your groups are around 1 MOA (1 inch at 100 yards). AFAIK, there's a decent rifle range up to 600 in Merrimak NH. If 400 yards are your desired maximum distance, look into a sturdy rifle in 223, when you think you're ready. REminton 700 and Savage 110 wont break the bank and will set you up for that kind of distance, if you buy a decent optic (which can easily cost you as much, if not more then the rifle of your choice).
What you are looking for to start with:
- Heavy contour barrel, free floating, if in your price range
- A smooth action (preferably bolt action to start with)
- A stock with a fair amount of stiffness
- A solid scope mount and rings (crucial for your accuracy)
- If you want presentable results, there's no way around good, and sometimes pricey ammo.
- Ask questions. The interwebs is an awesome place, where valuable information is plentifull. Try the forums at sniper's hide or sniper central. There are a lot of really good long range guys who share informations and give you the ability to learn from their experiences.
Take your time. Learn breathing technique, and get familiar with your system.