You are faced with a choice - which is the greater risk - losing people at the end of a (14 day - possibly some other period might be more appropriate) free trial when they have to convert to a paid plan, or losing people who have to sign up and start paying right from day one, with the offsetting promise of a money back guarantee. Both ways involve a point at which you will lose potential members.
I have no hard data on this, but intuitively think that if you truly are adding value, you are better advised to make it as easy as possible for you to demonstrate the value add you are offering. It is much easier to give away a free trial, and with totally no strings attached, than it is to say 'trust us, you'll like it, and trust us also with your credit card and your money up front too'.
Of course, you will lose people both ways, but don't you think you'd lose fewer people, and also have fewer problems overall, by giving the 'free trial - no need to even enter a credit card'?
The 'free trial, no need for a credit card' offer is really clean and shows a great confidence on your part, and also is totally transparent. Haven't we all come to be suspicious of the 'free trial and then automatic billing that you can never stop' type of trap that many services end up tricking us into (I'm trying to undo one of those myself right now that ended up with two $30 monthly charges as between when I said 'stop' and when the billing ended)? The very nature of the transparent honest and obviously impossible to cheat 'no credit card required' offer would seem to be a much more positive approach.
You'll note I hint at uncertainty as to the ideal duration of a free trial. Without understanding the product/service you're providing, the immediacy of benefits and how quickly people will get 'hooked' on your service, I sort of feel that 14 days is probably way too short. Certainly, if you are incurring direct costs, that will constrain your ability to be too generous, but if the costs are minimal, a longer period probably will be more enticing.
Lastly, while all of this is conjecture to start with, the good news is that is is relatively easy to try out all manner of variations, just by randomly routing prospects to different landing/offer pages. Assuming you have a reasonable flow of prospects coming to your site, you should try various offers. In that case, it might be helpful to store the initial offer detail presented in a cookie, so that if a person returns to your site three times he doesn't see three different offers - that would probably confuse and concern the prospect, and would also make it harder to identify the exact decision making process and offer response.