Note that you need to control 4 motors - not 3 - because one of the motors is for the extruder (and if you have more than one extruder, you will need to control those as well - but save it for the future).
The RAMPS board is not only a convenient holder for the stepper driver boards, but it also has connectors for controlling other devices - like the extruder heating element and the (optional) heated bed - as well as connections for temperature sensors (again for the extruder(s) and heated bed) and limit switches.
For the RAMPS board, it can use the A4988 and DRV8255 driver modules; the latter one is actually the one everybody is “upgrading” to, from my investigation into the subject. It has some features the A4988 lacks, and IIRC, it runs cooler, too. It’s drop-in compatible on the pinout, so if you start with the A4988, you can upgrade to the DRV at a later point (though the cost difference is minimal - so if you go the RAMPS route, buy the DRV drivers anyhow).
Stepper motors for most desktop-size 3D printers tend to be simple bipolar motors, of the NEMA17 or 23 sized frame standard, running at 5 volts and around an amp of current. They are easily found, and low cost, and most aftermarket parts aimed at the 3D printing community (pulleys, belts, shaft couplers, linear motion elements, etc) are sized for them. That isn’t to say you can’t use other stepper motors, just that the community seems to have standardized on one particular setup when it comes to desktop size machines:
Which leads me to the next question - do you have a particular reason to reinvent the wheel, rather than sticking with existing known working solutions? By that I mean mainly the software end of things; if you want to have a customized electronics hardware stack (in addition to the custom machine itself), have at it. But the software - that’s another different story. I’ve delved thru GRBL and Marlin, just on a lark. While it is very easy to read, it isn’t so easy to understand. There are more than a few somewhat obscure concepts and algorithms being implemented; I would suggest that if you insist on going this route, that you take the time and care to study the code that already exists. There’s a lot of hard-won knowledge involved and included in these pieces of software (not to mention the fact that there are a ton of derivatives and forks out there as well - for instance, Marlin descends from GRBL - in fact, quite a few descend from GRBL):
Furthermore - I would suggest that you do a lot more studying on the subject before committing to building your machine.
You might find it worthwhile and educational to use an existing machine - if you have access to one - and/or to build a kit machine first - before embarking on building your own machine from scratch. There are plenty of low-cost and good quality Prusa i3 machine kits on Ebay and Amazon - for most, everything is included for around $300 to $400 USD. You will definitely spend this much or more assembling your own system. What you gain from a kit is a better understanding of the mechanics and configuration of such a machine, and a realization on how much effort a kit will be to put together, to understand the level of difficulty designing and building from scratch will be. The Prusa i3 is also easy to understand from the mechanical point of view:
This isn’t to deter you from pursuing your own design, but more to make you aware of the amount of effort and knowledge that is in these machines, culled from years (over a decade) of experience by other users and builders. If you do insist on going at it from scratch, do take the time to do a ton of research on all of the components, sub-assemblies, operations, materials, etc. Go over the effort in your mind - design, construct and assemble your machine from a personal “virtual” perspective in your imagination. Work out as many problems and solutions as you can there, before committing to them in the real world. Gather together every document, picture, note, source code, etc - that you can get your hands on. Take extra care and time in the planning and staging of the project; doing so will help to ensure a successful outcome at the end.
You may have also noticed that all of the links I have posted have been to the RepRap site. There’s a reason for this, and it is to illustrate the wealth and depth of knowledge housed on that site. Those pages are but a small portion of the overall amount of information you will find there. The RepRap forums, as others have pointed out, is a thriving community of makers and 3d printing enthusiasts who represent a living legacy to the technology, craft, and experience; if you haven’t explored this resource, I highly recommend that you do so. Not having knowledge about it, what it offers, and such - would be like buying an Arduino and never visiting this forum or the arduino.cc web site. It wouldn’t make much sense, and you would lose the opportunity to gain a wealth of understanding that would come with visiting.