So, the bossman wants to set up a website to sell some of our smaller stuff. He asked me to research how to set up the necessaries (shopping cart, method of accepting credit cards, etc). I have no clue where to even start... anyone have any experience with this sort of thing?

I setup quite a few of these for a living. I've used osCommerce sometimes, but it's a horrible mess. Check out http://www.magentocommerce.com/ for a sweet system.

most host have built in webstores you can setup along with a cart, if you host your own site then there are a slew of apps you can go with based on your webserver.

most these apps provide a conduit to validate a credit purchase online but you'll have to get a cert on your server.
much easier to use a hosted one, cause in not there are new rules regarding securing the credit card numbers and encrypting them so no one can steal them and use them.

I've been trying to push Mark (my boss) toward an independently hosted solution, but he's got this crazy idea that it would be better to buy a program and upload it to our web host...

that's an option but your host will have to support it plus you'llhave to get an ssl cert and you have to make sure it's secure.
if your host has a built in cart with support for secured credit card authorization and transaction then that's fine, if not find a host that does.crystaltech has a couple of carts that you can use that's pretty easy to setup.

Argh... so this came up again today. I think he thinks I can just download some magical thing off the internet and install it, and we can be up and selling stuff online by tomorrow or something. I really don't feel qualified to be handling this, but when I say so, I just get the "Well, with a little research I'm sure you can handle it!"

repeat after me...

Mark, we need to talk, and i need your attention.

sit him down, explain to him that its not a matter of research, but that what he thinks he wants, is not what exists.

explain the options.

pretend you're talking to a llama at a petting zoo if you need to.

yes, its a pain in the ass... but you will be far better off in the long run having explained it now.

you're in a unique position to be royally kicked in the ass here. the last way you want this to turn out is... you ignore his incompetence, say to yourself "i'll do what needs to be done and not bother him with details that he won't understand". start doing it, and when it seems to take up a lot of your time, he starts asking questions.
and now you have to have an explanation for the worst of questions... "i told you to make an online shopping cart... why are you doing all this? wasting time, not doing your work, if you couldn't do it, you should have told me, and we could have found someone who could."

don't put yourself in that position... seriously, you don't want to be there. thats how murderous rampages start.

first, he needs a Paypal account or a "internet merchant" account from his bank.

If you don't go with an online storefront system, you can use templates in Dreamweaver or most good authoring tools
But...

to have a shopping cart system that's done by yourself your site has to be hosted on an ISP that has Perl/PHP/or some other engine parser available to keep data active between pages.

most only allow simple cgi, which won't cut it.

For simple things you could make a php cart system and calculate totals, and send it forward to paypal

but again, if you don't have the parser on the server you can't create the active cart system and feed data to paypal...

An already existing system is faster to get going with, I think you can look at paypal, they might even have a "shopping cart" merchant system, but your bank might as well, and it would fit into a frame on your site....

some things to think about

I did s site with a shopping cart back in the day for someone
turned it over to him to input all the stuff for sale & prices LOL it just sat online with nothing to sell except for the few things I listed .
setting up a store front online is a pain in the ass when you first set it up
the real work come in adding everything your selling to the database
man at that point it's like a data entry job
Boring as hell & takes a bit of time
you need pictures & descriptions blah blah blah
if thats not your thing then stay clear of it

This hasn't been mentioned for a while since I laid out the facts to the boss man, and I'm hoping maybe if no one says anything the idea will go away...