Hi Mr.Snrub. Welcome to the forums. 
I’m no expert here, but let me try to give a starting answer to some of these questions.
how the different types of ecommerce software work (i.e. Magenta, PayPro Global etc. ) – how they integrate with the site, and how customizable they are etc
Well, there are various different approaches to ecommerce. Let’s start with shopping carts.
There are, for example, some software packages (ecommerce CMSes) that form the basis of your whole site. You style them to suit, and they have a whole range of functions in-built—predominantly geared around a website for selling things. So they are basically a ready-made website that you style to suit. Examples include osCommerce, Magento and ZenCart.
This kind of software package you install on your own web hosting account and manage all yourself—including security. However, that’s not the only option. Some companies, like Shopify, allow you to set up an account on their servers, and they handle all the security, which is a big bonus. You just pay a monthly fee, and all you have to worry about is uploading images etc. However, this means that you don’t have total control of your site, and don’t choose your own web host etc. These services look after your entire website.
A third option is to build your own website in any way you like, and to use a third party just for the shopping cart. Examples include FoxyCart and eJunkie. Whereever you want to sell a product, you just put a PayNow button on your site, and it links to the third party site. The better ones let you style the landing pages to look exactly like your website, so that customers have no idea they’ve actually left your site during the purchase process. The simpler ones, like PayPal, make it quite clear to the customer that they have left your site for the purposes of the transaction.
Now that is just software for setting up a website. The actual precessing of payments is something different.
Most of the time, there are three factors in the online payment process, usually provided by different companies. First, there is the shopping cart. As described above, that may be software installed as part of your own website, or a whole service provider like Shopify, or a remote, third party service like FoxyCart.
Either way, once the customers have added a product to the cart and are ready to pay, the transaction has to be passed on to a “Gateway”. This is another service provider that is authorized to process credit cart details. Examples imclude Authorize.net and Eway. These gateway providers are a separate service with their own, separate fees. 
Lastly, the money collected by the gateway service has to be deposited somewhere, so normally you also need a merchant account at a bank. This is different from a normal bank account, and also has its own **** fees. 
So, in most cases, you have two or three services taking money from you—two if you install your own software on your website (but then you have security to worry about), or three if you choose an external service provider to which you pay a monthly fee.
The exception is a service like PayPal, which is a bit basic and clunky, but which incorporates all these levels of the transaction—cart, gateway and (sort of) bank. You just have to transfer the PP funds to your regular bank account—though, you guessed it, at a fee.
what programming languages whomever [sic] programs the site will need to be proficient with
Doesn’t really matter, but most commonly it’s PHP. Most will just use a CMS, though, which is normally writ in PHP.
the difference in payment systems and how customizable they are i.e. do they integrate into my website, or does to customer get transferred to their website (PayPal style)
Hopefully my answer will have covered that to some extent. How customizable they are depends on the service. At the lower end, you have PayPal, which is barely custmizable at all. At the other end, you have the CMSes, which you can often style to your heart’s content.