Choose which one comes first. You can't choose both.
Personally, I'm designing for success. I want to make a bit of money, and have achieved something. I want to be able to call myself a published board game designer. It's a competition, and I want to win. I do enjoy game design a great deal, but I get enjoyment from working towards the end goal, which is publication — hopefully very successful publication.
If no one's ever going to see my game, outside of a few friends, it's a meaningless exercise to me.
You might be designing for enjoyment. You might have this idea you've always wanted to make, or maybe you want to challenge yourself, like seeing if you can redesign Magic, but without the "mana screw" problem. Maybe you have this great vision you just have to put into reality. Maybe you just like the process, and enjoy working on something. If this is you, you must be absolutely prepared for your game to eventually go to its permanent resting place on your shelf. When I talk to amateur designers about this, many of them hadn't properly come to terms with this inevitable fate for their game.
Just because something is an interesting idea for the designer, doesn't mean it's going to be fun for the players.
I've seen all kinds of ingenious ideas that belong in an article, not in an actual board game.
You need to ask yourself if your idea is something you just want to make because it's a challenge, or because other people will enjoy it.
You might be designing a game with some crazy constraint, or a variant of some game BUT with or without some feature. These are not going to lead to publication.
This musing leads me to a very important point. You are one of these two things. I've seen numerous people design something purely for their own entertainment, and then spend vast amounts of time, trying (unsuccessfully) to market it. You will absolutely not succeed at this, in a very tight market full of people with realistic approaches to publication.
If you're serious about game design, you need to take a ruthless, business-like approach to game design. Success equals getting published. If you don't get published, you have failed. Always design games strongly leaning towards themes, components, and other characteristics, that will increase your games' chances of getting published. You do what the players like, not what you want. You polish your game to the nth degree, and you make a heap of games, to increase your chances of making something good.
You can't put off answering this question, or simply live in denial of its existence. This choice has impacts on fundamental parts of your game design.
You're in this primarily for success or fun.