Faulty Battery :( Purchase from dealership?

Hi Everyone!

Just to recap, I wasnt sure if I previously had a battery issue or alternator issue. Well, I finally bought my car into my shop and they told me I had a faulty battery..

Problem is, that they want to charge 600$ for a new battery and installation. Plus $120 to look at the car, so a total of almost $720CAD!

Is that worth it?

Or am I better off sourcing my own battery and putting it in myself? (My boyfriend is able to put the battery in for me if I need him to)

Thanks in advance for the help

Also, if I were to source my own battery... any recommendations on a good location in vancouver bc?

i saw in a previous post that I would need

110AH regular Bmw battery
or
90AH AGM Bmw Battery

Does it matter which one I get?

My battery is charging but it is old and weak. I plan on purchasing the battery from Autozone or Advanced auto parts here in the USA aproxiamtely $200 USD. My car is a2005 645ci, it requires the new battery to be coded in. An independent shop will code the battery at an hours fee $60-$80 USD here in my area.