If you get the error "Blender - Can't detect 3D hardware accelerated driver" when opening the application then you need to make sure your computer meets the minimum requirements. View the information here:
You mainly need to make sure that your graphics card supports OpenGL 2.1. You can check your graphics card by going to the Device Manager and viewing the information under the display adapters.
If you are using an integrated Intel graphics processor you can check this website to see what version of OpenGL is supported.
If you have a graphics card that supports OpenGL 2.1 then you might just need to update your driver.
It is best to go to the manufacturers website to download their current driver.
Overall, you don't need an expensive graphics card to run Blender. Typically, if your computer was manufactured in the last 10 years everything should work.