Your Blue Screen could have a number of causes, but none of them would carry across to a new machine unless you move some component (or software) across. It would be good if one could identify the actual cause of the blue screen, because that would influence the decision.
But before you throw around lots of much needed dollars, let's think this through first:
To give you a few ideas - a "popular cause" is a flakey memory module, sometimes only acting up under thermal stress, which could then be explained by a failing fan, or flakey power, or corruption on your hard drive - any of these and many more can be of a temporary nature, so it is quite possible that you get a blue screen a day, but your computer guys get only one a week, because their office is generally cooler than yours.
Their tests should have included a memory test as well as checking out the fans in your computer and verifying that the power supply is producing all the right voltages under all normal conditions.
A power supply is quick and cheap to swap out on most "normal" machines, running a machine for a while with reduced memory capacity to exclude a faulty module is also not expensive (you may want to "top up" your memory after you have identified the faulty component.) If there was corruption on your disk - which can happen without the disk going bad, simply by a power failure or surge at the wrong moment - running a "repair" of your WIndows might solve the problem and that is something that a savy friend might do for free and your computer people might do at a reasonable price. Unless you actually _want_ a new machine you should try these before spending any real money. I know your computer shop people said that there was nothing wrong with your machine, but from a distance and with some more experience I think we are allowed to take that with a grain of salt, especially from someone that wants to sell you a 500GB SSD as a solution. Now, a 500GB SSD is a really nice thing but it won't fix your problem any better than the alternatives.
Let's see: You will be impressed with the speed, but speed wasn't your problem, right? Installing a fresh copy of Windows may well fix the problem, but it will be a lot of work to reinstall all your software. If a repair of the existing Windows works you have solved the real problem much quicker and for much less money. It would only take a few minutes. Then, to check and - if need be - replace fans is also a lot less of an investment and if you did find a bad fan you will know that you fixed a real problem.
In fact, come to think of it: If you decide to spend money, get a new or refurbished machine and see if you can't find a community project near where you live that would be interested in your old machine - some of these will find volunteers that can fix the machines for the use of the project or as donations to needy families. Where I live some of the good work of these projects involves teaching youngsters computer skills in the process of repairing older machines, also by mixing and matching components from several machines to bring as many of them as possible back to life. You may even decide that it wouldn't be half bad if you had a backup machine yourself ...
But before you spend significant sums, be sure you understand fully how that will fix your problem. Example: If your existing disk drive isn't broken then replacing it with a big SSD won't fix anything, it will just add a "nice to have" component. Or - a complete reinstall of Windows: that could also be done on your existing hard drive (or a new conventional disk or a smaller and therefore much cheaper SSD) But the repair that I suggested is likely to accomplish the same thing and doesn't cost anything except a bit of time.
There is another thing you might want to do: Try and figure out if the shop people were seriously trying to sell you an expensive (if nice) piece of hardware on purpose or if some techie's own dream of the ideal storage solution was getting the better of him. Depending on that I would consider checking out other stores in future.
Then - once you come to the conclusion that you can't avoid throwing money at this -