Customer registration/order form/plug-in

Hello all!
I am in a bind and the google isn’t doing it for me right now. Maybe I am searching the wrong keywords, whatever. I figured why not tap the very community that is here on wordpress (smart logic right haha).

Here’s what I am trying to do…

I am putting together a website through wordpress that I may skin myself or theme and here’s what it needs to do:
– When customers/clients come to my site, they need to register/create a log-in
– the purpose here is some that I may build a database of said client info.
– I then need to infer to be tied to what comes next… (so my understanding the registration creating creating log in info would be best)
-I need a form the customer fills out to provide me with the details of the services they want.
-I will not be taking payment information or processing orders from the site. this will be done personal once I obtain the info they provide me through the site. so commence in the payment sense is not necessary.

So simply put… I need to figure out how to implement a site that will allow people to register, giving me a database of their information, that is in turn then connected the to order they submit through a form of some kind. They register then order and they details are sent to me. Next time the visit they just need to log in.

Hope that makes sense. I apologize if this sounds repetitious.

Any ideas?!?!?!

If this requires plug-ins, what are they? I don’t mind paying if I have to. I accept not everything is free haha.

Thank you all for taking the time to read this at the very least!