Different people react to cannabis in different ways, and every situation is unique. I've met some people who don't like to get very high because they get a similar paranoid feeling to what you were describing, and here's what I've seen them do to help.

1. Smoke less, especially if you're just starting out... if you're smoking dank (really good weed), then one hit will probably get you pretty high if you're new.
2. Make sure that when you smoke, you don't have anything you need to do for at least 4-5 hours. That will give you more than enough time to calm down and feel completely sober before you need to worry about doing other things.
3. Surroundings make all the difference. If you're getting high with people that you know and trust, it is much easier to relax. Try putting on some music and have a conversation.
4. I don't think how you smoke will make that much of a difference in your high, except for in terms of how much smoke you actually inhale. With joints, you get a mixture of weed and paper smoke, and it can be more difficult to judge exactly how much you've smoked. I'd recommend sticking with that glass pipe for a while, until you are a bit more of a seasoned smoker.

Hope this helps.