Terminology questions (DNS, A-records, MX records, Static IP, etc)

[Web Guy]

I'm shopping around for an ISP that will provide DSL service to a
small business.  The business is running a couple of PC's (one with
SMTP software, the other an HTML server) plus a handful of user PC's,
all part of a local network.  The business has a registered domain
name.  Let's say the domain name is "acme.com".

I do not care at all if the ISP is providing any e-mail addresses, or
web-site hosting space.

What is important is that e-mail sent from anywhere on the internet to
"someone at acme.com" must find it's way to the SMTP server mentioned
above.  I believe this requires the ISP to have appropriate MX records
which are located on their machines somewhere.

Web browsing to "www.acme.com" similarly must be resolved to the
dedicated IP that has been assigned to the business.

Question 1:  What is the name of the item or service I require from
the ISP to accomplish the e-mail connectivity as described above?  Do
I require "MX-record service" or an "A-record" or what?  What is the
correct name or description of that item?  And is it typically free,
or is there a monthly charge associated with it?  (or is this a
function of the domain registrar?)

Question 2:  Similar to question 1, but with regard to HTTP
functionality (which I believe is generally known as DNS resolution to
the assigned dedicated IP).  Again, what is this item called, and is
it typically free, or is there a monthly charge for it?

PS:

The reality of the situation is that the business currently has ISDN
service with a block of dedicated/static IP addresses.  There is
obviously some MX and DNS records somewhere that are correctly
configured because e-mail is being received and web-site access is
currently happening as described above (although I think that reverse
DNS on the IP address of the SMTP server is not set correctly, which
means that very rarely an e-mail sent from "acme.com" is rejected
because of this).  The domain name is registered with Network
Solutions, and I am registered with them as the primary contact for
the domain.

I basically want to replicate this situation with a new ISP on a
single dedicated IP, so I need to know what to tell the ISP I need
from their end.

Thanks for any replies (please post them, don't try e-mail).