Two Easy Questions (for those in the know)...

1. I run an Internet business (Registered as an Single Member LLC -
will file Schedule C) -- where do I report my costs paid for shipping
to ship merchandise? Does this go under shipping or others?

2. I live in state of CT -- was I supposed to be filing quarterly
(only had a couple sales actually from the state of CT), or do I just
do my taxes regulary each year with my Federal.

For the first question; yep, just put an entry in the
deductions area called "shipping" and total you shipping
expenses there.

As for the second question, you might check out the info
I dug up for another question as you might be responsible
for collecting sales taxes for Connecticut:

According to: http://www.vertexinc.com/cybrary/internet/tax_table.asp 
 
All states except the following have state sales tax on internet sales: 
 
Alaska 
Delaware 
Montana 
New Hampshire 
Oregon 
 
More information (state by state) at: 
 
http://www.vertexinc.com/cybrary/internet/state_by_state.asp

I'm not so sure I'd agree with the table denco-ga has referred you to.
 I also run an Internet business based in California.  I had the same
question, so I called the California State Board of Equalization (who
collects sales tax for California). Generally speaking, freight
collected is not considered part of revenue.  However, there is a
caveat. The shipping that you collect has to be equal or less than the
amount you paid for shipping in order to avoid calling it revenue. 
Additionally, there must be documentation on your order that
specifically says "x" is merchandise and "y" amount is freight
charged.  It gets a little tricky.  The best thing I can advise is
call the taxing authorities for the state you live in.  That way,
you'll get it from the 'horses mouth.'  You should always get an
answer from the taxing authorities in writing.  This will be needed if
you are ever audited and the auditor disagrees with your treatment of
the freight.

Hope that helps a little. Good luck.  Taxes...bah humbug....

Well, Schedule C is pretty straight forward.

Any income you derive (money coming in, etc.) would
be on Part I (Income) Line 1, which would include
the shipping and handling charges that people paid.

Part V (Other Expenses) Line 48 would be where you
would put the actual shipping costs you incurred,
and that number (plus anything else in Part V) goes
on Part II, Line 27.

This way any actual (net) profit you might have
made from S&H charges flows to the net profit, which
then flows to your 1040 return which flows to your
state tax return.

You might have to file a separate form for the state
as well.

The link that I provided:

http://www.vertexinc.com/cybrary/internet/state_by_state.asp

might indicate you have to do sales taxes as well,
which can be quarterly in some states, and yes,
respree is right in that you should check with the
state to see if S&H is sales taxable or not.