I don't know much about Magento so I need some advice. I do know PHP.
A client wants to update their website to ecommerce and use Magento as the framework but they want to use their current accounting package for user logins, products, orders account, etc because the data is already there.

So, what is the best way to tackle it in Magento? Should I be looking at doing an entirely new custom module or overriding the existing code for database queries? Like I said, I don't know much about Magento or its internals so I'm not even sure the second option is feasible...

Any advice from people that have done this (or are just familiar with Magento)?

You're in for one hell of a ride. I briefly looked at using magento but on downloading the files of which there are literally thousands I gave it up as a joke.

well, thats encouraging...

Magento is pretty much follows the same MVC pattern as Zend framework. You will need to have some really good understanding on how MVC pattern works.

Thats fine, I just wanted so advice as to whether a custom modue is a better approach than tearing out the product/account fetching code that is already there and replacing it with queries for the third party accounting package.

cool fair enough.

One of the many ways of doing this for your purpose is to create a bridge between the existing database and the magento database.

It's been a while since the last time I was playing around with magento. Although I still know the basics construct, I can easily get lost at this time.

As far as creating a bridge, I completely forgot how I did it, it was long long time ago when I was a sophomore in high school. I remember writing a bridge for the SMF (simple machine forum) and the phpBB forum. The bridge was intended to use the existing phpBB database in SMF forum environment. The most challenging part was the authentication of the users.

I am sure the process will be pretty similar.

Here is a good start about multiple database connection in magento.

I honestly think that you might be better writing your own e-commerce platform. The worst thing that can happen is if you start doing this in magento get half way and realise you've bitten off more than you can chew.

Magento has a steep learning curve. I'm talking 6 months minimum to learn. And there are literally so many freaking files.

Let's think about what you would need to create your own shopping cart. Products, product options, product categories and price.
Then you would need a table to store purchases and a script to tie in with paypal. I'm in the process and it is not that difficult, plus I know exactly what it is doing and how to customize the front end.

You can grab a html theme from themeforest, then just populate it using php.

My other option would be to use opencart, if you're using to a framework like codeigniter you're half way there.