If you don't have someone to help you out, fixed pitch is definitely better to start as it's way more simple, no throttle/pitch curves to adjust, no pitch adjusting etc. Plus, since it has less parts, it will be more durable. A fixed pitch heli will help you learn to hover and get you familiar with a heli and the controls first, although a fixed pitch is harder to fly especially in the wind. Reason being is that you have to decrease rotor speed to descend and the lower the headspeed, the less stable the heli becomes, couple that with some wind and you're in for some sticky situations . Definitely stay out of wind when you're starting! If you have somebody who's a little experienced with cp, go straight to cp, the difference in the control you have over the heli with cp is huge.

Definitely get yourself a heli radio like Sabot suggested, you will later thank yourself when you get a cp heli if you don't get one from the start... As far as soldering, a soldering iron is super cheap, you will need to get one and learn to solder if you're gonna stick with this hobby, there's really no way around it without sacrificing performance and reliablilty.

If you don't have anyone to help you out, I'd recommend the Corona for a first heli. It is a fp and very durable, it is absolutely a great heli to learn with and should fall into your range with everything. If you're starting from scratch, you may be looking at a little more than your stated budget because you will need to get batteries, charger etc. The main thing is don't skimp on a radio and get a good head hold gyro, it will help with the learning process and you can use it on later birds.