Once you get to a stage (and save) you'll be able to select that stage at any time from the main menu. However, be sure to save! The game will ask you to save if you either lose all your lives and choose not to continue or if you quit the game from the pause menu. The game does not auto-save after beating a stage (not sure about the whole game--haven't beat it yet) so you must manually save.
I just beat the game. (Very satisfying boss, if a little too familiar!) I can confirm that the game prompts you to save after the credits.
I wholly recommend this game to anyone who's a fan of the classic Castlevania games (or challenging 2D platformers in general)