This totally depends on your project. Likely they will have very different needs. If you are looking for something that needs actual computing power - say a media server or something to run retro emulators on, then you are going to need a Raspberry Pi - get the latest, most powerful model you can afford.
If you are looking to use a board for a specific, single-minded task, that is more actual code-orientated, then an Arduino of some form or other is ideal. Simply carry about a little research on the type of Arduino you need - there are lots, all offering different features and coming in at different prices and, most importantly, go and have fun in your new Maker hobby.