Sealing inside of external brick wall
Ok, I guess you have to acknowledge that preventing water from reaching the wall is the best solution, followed by exterior wall protection, but I read the OP as acknowledging this already and asking specifically for interior solutions to water proofing.  Since you mention being a software engineer, I see it analogous to a question about cryptography, where you're not necessarily looking for something that's 100% unbreakable, but simply what's appropriate for the task at hand.  Really awful images can come to mind when someone says "Moisture seeping through", but it seems to me like we're not talking about standing water on the basement floor, just the presence of moisture on the wall (correct me if I'm wrong), and a partial solution able to be implemented on a short time frame (1-2 months).

I recently did some work on my basement brick wall where I have a little bit of moisture seepage and efflorescence, nothing serious, just a little. I stripped the brick clean and used Quikwall over it with an acrylic modifier, and with a sealer over that.  This has worked well for me since I'm not trying to hold back floodwaters, I just want to limit efflorescence. 

I never heard of tanking slurry, but of course I did a quick Google search and can now talk about it like I'm an expert :)  Ok, but really, I have heard about similar products before and understand the science behind them well enough and it's theoretically solid.  It sounds like it'd work well, and I know there are an number of similar products out there (not sure what's best). I may end up trying it myself. You can also coat your floors if you see a need to.

A couple additional notes. Sounds like you plan on finishing with plaster.  Quikwall can be used as a plaster like finishing itself. If you plan on finishing some other way, I've used RedGuard before which helps prevent cracks and is very effective at water sealing, but is bright red so is not a good finish on its own.  Also, the other (although much smaller) cause of basement moisture is condensation, which you can't seal against, so there are situations where insulation is used to protect against that.

The OP also asks about cost. I'm not aware of any cheap solutions that delivery a reasonable level of effectiveness.  From what I've seen, it costs money to do anything you're likely to feel comfortable with.