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It depends on what the differences will be. Will you be able to play multiplayer modes in singleplayer against bots, for example? Although, from my very limited experience, it's probably best to design the game with multiplayer always in mind. This way, you don't need to re-work all your core game logic for multiplayer. You have a base which works for both and the only changes you need to do are in how you interact with it based on singleplayer vs. multiplayer, e.g. how do you handle spawning the player(s), losing, restarting, etc. Pretty much anything that must inherently be different in one mode compared to the other. It's a bit more work in the short run but in the long run it pays off.

I might be missing the point of your question a bit though, since your question is more about the content now that I read it again. As for what you should do first and what matters to the consumer, I'd say that engaging singleplayer levels would be better to start off with as it is more accessible, seeing as there's no need for other people to play it in order to enjoy it. Also from a development perspective, it's gonna be easier on you to playtest and experiment and just make the game more fun in general. If you have a fun singleplayer experience, then people will start wanting multiplayer. Multiplayer for the sake of multiplayer is not what people want.

So, in summary, design everything to work with multiplayer to save yourself some pain later on, but focus on singleplayer content first. Get lots of feedback before starting work on multiplayer, so that you have a solid base to expand from.

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Thanks Kaktusz, that was exactly what I was looking for.
So I started to add multiplayer support for the single player parts I've already done just so that everything also works in online too. I'll focus on the single player game first and will expand it from there.

Also the game took a big leap sideways and it's now 3D instead of boring old 2D. Check out the difference here