You absolutely want to be able to choose grind size - even if you have a preferred brewing method and beans, you still want to be able to make some adjustments up or down if necessary. Even more so if you are going to experiment with brewing methods, where the required grind size ranges from super fine powder (Turkish Mokka) to coarse grain (cold brew). And it is a good idea to pick a grinder that has its strength at the coarseness you need most - few will actually cover the whole range.
That said, the really important detail is how homogeneous the grind is. If you have a wide range of particle sizes, you will get over and under extracted coffee at the same time and it will be a compromise at best.
That’s why I would strongly recommend that you invest in a burr grinder, that should be the kind where you can set and adjust the grind size. As said before, read a few reviews before selecting the model that matches your needs and budget.
Blade grinders work like food processors, chopping up the beans with a rotating knife and the longer they run, the finer the grind will be - so the time you run them is sort of a grind selector. By design they produce a less homogeneous result (depending on how the blade hits the beans, some particles will be bigger, some smaller), which will sometimes work for coarse grinds, but not for fine ones. They are often cheaper, though, which is why some users pick them over burr grinders. I would not choose one if possible.
There is a reason why some pros recommend to spend equal amounts on your grinder and your espresso machine. If you are brewing with a low-budget method (e.g. pour-over by hand), the grinder will likely be the most expensive piece of equipment - and probably worth the investment.