Use Google Forms. It works well to conduct surveys. They have lot of the functionality built in. You can use it for a number of other things as well.

Google Forms for the extremely pragmatical or http://www.typeform.com/ if you want something pretty

I would recommend you look at Gravity Forms which you can use on a Wordpress framework. The forms are easy to put together, and have a great deal of flexibility and options for integration with other platforms. You can easily use Gravity Forms for multiple stage forms.

There are plenty of options, including WordPress plugins: Gravity Forms is powerful.

JotForm.com is GREAT! I've been using it for years and it keeps getting better. The whole thing is drag and drop and you simply add a line of code in a wordpress page or post or other site and the form appears. When you change the form it updates on your site. I use it all the time.

I've tried LOTS of options, but never had one work so well. It's one of the few services that simply works the way it is supposed to so I keep using it.

Also, Zapier (which I haven't used as much) links your forms to other places you need data.

Here are some sample jotforms:

http://mikemoyer.com/contact-mike/
http://www.slicingpie.com/feedback/
http://www.34701.org/fall2014/last-class/

The best way is to rely on an easy-to-use online tool that walks you through the entire process. The site should take the guesswork out of the whole thing. I'd suggest using http://www.fieldboom.com/ to create advanced forms because it does all of those things. You can even try it out for free to see if it meets your needs. And if you ever decide to do a survey, it can help you with that too.