It is not just a matter of buying a graphics card (because you really can’t install those in a Laptop) you will be purchasing a device that is a little box that houses a graphics card but connects through a high-speed port. Since you are inexperienced with personal computers, I strongly recommend finding someone in person who does have experience. Either way, it will cost money. To further complicate things, getting any form of a good graphics card directly is expensive as there is currently a bad trend of people scooping up GPUs solely for the purpose of cryptocurrency mining.
Most computers that are priced around or more than the cost of a gaming console should be capable give or takes. For you, this may be the better option and it will keep things easy, while it would spend a little more money upfront, you will future proof yourself a lot more. Note it can be a little cheaper to get a desktop for your gaming needs over a laptop, so unless you travel frequently, I would recommend a desktop.
I recommend shopping online for “gaming pc” and keep to a $500 to $600 price range. Most PCs I have seen there easily meet Overwatch’s system requirements. You could go cheaper but be conscious of the system stats at that point. Note that if you are interested in more hardcore gaming experiences such as Virtual Reality gaming like HTC Vive, you will need a system with a more beefier graphics card and be pushing to the $800 to $1200 range at that point.
This probably sounds overwhelming and you will need to carefully consider your options to your budget. However, the PC platform is a great way to play video game in its own right. It doesn’t replace consoles, but opens the door to new adventures and fun (not to mention the entire library of Blizzard’s current game lineup).