Ah sorry, ABD - I somehow thought you would be doing ecommerce sites for others, with someone as staff, and wanting to know enough to know if they were building sites for others using suitable methods... Sorry, my misunderstanding.
Given I now understand better - then learning how to use DW and anything else (JavaScript, PHP, Perl, Ruby on Rails, Joomla, etc, etc, etc) could be a complete waste of time, if the site built for you uses none of them...
If you're planning on taking courses, it's only going to be worthwhile if you were going to use it yourself (IMO) else you could buy some appropriate books when the site is being built, to see if you can follow what's being done... and it may be very technical.
I look at lots of sites to see what's going on, and it is usually very tricky, the more so when the data being displayed is pulled from a database (such as happens when a blog is displayed, newspaper articles, photo galleries, any site which has dynamic content, and so variables will have different content for each page, even if the same code is used every time.
When I say "look at lots of sites" that may include extracting all the CSS and JS files, but anything running with MySQL (db) will have content that appears on a web page but clearly one never sees the code used to extract it.
I also install (from cPanel/Fantastico) various PHP packages (free, but source code is under GNU licence so could never pass off as one's own) just to look at the source code, change colours, replace animated GIFs with static GIFs, etc, to tailor to my needs, and learn about the techniques used.
I have 4 shelves of books and several GB of electronic books about coding and have been in IT 30 years but still regularly find stuff which I cannot figure out without taking days or weeks researching. So sorry, but not being involved with e-commerce, I'm not much help, but foresee you having considerable difficulty in understanding, as a non-web designer/programmer, exactly what goes on, without a hefty technical manual being written (which is unlikely to be part of your requirements for the site, or the quote(s) you received).
Up to a point, you are at the mercy of the designer - some web designers use T+C to restrict maintenance to themselves, and never pass 'ownership' of the code to the customer. It's unscrupulous, but may happen without the user considering it (similarly with copyright - in my view it should rest with the buyer of the service, the end user, but I've seen reports of complaints that web designer claimed copyright and when some dispute arose, domain owner found he'd be sued if he used the same graphic elements and site had to be built new from scratch - again, not something I'd 'forecast' for someone - but if there's a multipage contract, make sure you own everything afterwards and aren't locked into a maintenance contract at rates which can change later.
If the web designer is open and up front about either having a fixed fee and it's all yours, or a reduced fee and monthly/annual fee which includes maintenance, all well and good. If it's hidden in small print, then carefully look at the rest of the small print.
My clients get the source, on a CD, in case I'm hit by a bus. They can then upload on another host with minimal changes, and hopefully all would return to normal (less me!)