Loadout should be original sniper, jarate, and bushwacka. The normal sniper rifle can kill anything quickly provided you aim it right, and jarate and bushwacka compliment each other nicely for your close-range defense and team support needs.
Here's something you should remember that I don't think anyone has mentioned yet: Don't be afraid of using bodyshots. When dealing with soldiers, demos, pyros, and scouts especially, well-timed bodyshots can mean the difference between life and death. If you manage to pull off a headshot on one of those first three classes, another shot anywhere will most likely kill them (unless they're overhealed or you get unlucky against a soldier). Use damage displays to your advantage and try to keep track of your enemy's health so you can know what kind of shot you need to make.
Practice your no-scopes. Without an SMG, the sniper rifle must be your defense at medium range as well as long, and being well-practiced in no-scoping will make you far more effective in close-quarters. For example, if you happen to find yourself caught by surprise and being chased by a pyro, it only takes four no-scopes to kill your enemy from full health--and that's without using your jarate. Scoring hits on potshots and quickly switching to your Bushwacka will make you a force to be reckoned with when you find your opponents closer than you had hoped.
Lastly, pay attention. You may think that you do already, but there are some things most people overlook that a good sniper doesn't:
-Listen. The sound of footsteps on surfaces you know are nearby, or of cloaking and decloaking, can help you prepare for a sneak attack, and nullifies the element of surprise that spies rely on to kill you. Listening to the sounds of nearby gunfire can also help you know what's coming your way.
-Keep track of teammates around you, where they're going, and who's dying. Not only will this help you spot spies, but you can also tell where your other enemies are by keeping track of who's killed who.
If you pay attention, you have no reason to use the Razorback, and you'll find yourself killing plenty of unaware people who think they're catching
you off-guard.
Don't forget to play on Black Mesa! The best snipers hang out there.
4. Be like me

I have no problem with snipers. Just spies. I can take 1 on 1 and win with any sniper.
Doubtful. >.>