In overall, issues you will end up running onto will depend on you and your approaches. Friend tends to say that complex is simple from different perspective.
Choice of graphics library depends about what kind of game you are going to write? OpenGL is common choice in this kind of projects, but you could also use some GUI-library or directly just use windows' or xorg's own libraries. If you are going to do fancy, just use OpenGL.
Questions you ought ask:
Is C++ sensible choice for this project? Consider C and/or python as well. My answer to this would be that if you just want to write reversi, go python. But if you want to learn a low level language, do C first. C++ is an extension to C, therefore there's more to learn in there than there's in C. And to my judge, the more you have to learn onto C++ is not worth the effort.
How do you use the graphics library? If you are going to do fancy effects, go to the scene graph. Instead you can just render the reversi grid with buttons on it.
How ought you implement the UI, should you use the common UI concepts? Usual UI concepts (windowing, frames, buttons, menubars, dialogs) aren't so good as people think they are, there's lot of work in implementing them properly. Apply the scene graph for interpreting input and try different clever ways onto controlling the game. Avoid intro menus(they are dumb and useless work), use command line arguments for most configuration.
I yet give you some ideas to get you started:
Othello board is 8x8, 64 cells in overall. You can assign a byte per each cell, that makes it 64 bytes per each board state. It's 8 long ints, not very much at all! You can store the whole progress of the game and the player can't even notice it. Therefore it's advised to implement the othello board as an immutable structure which you copy always when you change a state. It will also help you later with your AI and implementing an 'undo' -feature.
Because one byte can store more information than just three states (EMPTY, BLACK, WHITE), I advice you will also provide two additional states (BLACK_ALLOWED, WHITE_ALLOWED, BOTH_ALLOWED). You can calculate these values while you copy the new state.
Algorithm for checking out where you can put a block, could go the board through one by one, then trace from empty cells to every direction for regex-patterns: B+W => W^, W+B => B^ This way you can encapsulate the game rules inside a simple interface that takes care of it all.