Well, the phrasing makes it sound like you want to get both eventually. So it might just make sense to get them at the same time so they grow up together and familiar with each other from a young age. If that's not possible I'd probably suggest making sure you get them so that the dog gets used to the cat from a young age - so probably second (i.e. get the cat first then get the puppy later, and the puppy will acclimate from a young age). If you introduce a cat with an older dog, the dog may see it as prey (especially if a smaller cat and larger dog)...
In more general terms, cats tend to be a little more independent at an earlier point so may be easier to manage in some respects, although they do still need regular attention and play (and of course appropriate grooming and feeding and regular vet checkups). But they can reasonably be left to their own devices for fair chunks of time once litter box trained (e.g. the length of a work day). This makes them a bit more accessible for a lot of people who have to work regular office hours or similar.
Dogs on the other hand pretty much need near constant supervision - a dog is a lot like having a small child around really. If you aren't working from home and can't go home at lunch to let them out/feed them/give attention, you will probably need to find a dog sitter/walker (or family member) to do that. To a point you can leave them for longer periods but they tend to not manage it as well as cats to my knowledge (and are more prone to destroying things while you are out if not getting enough attention/exercise, and more prone to "accidents" indoors if there isn't someone to let them out regularly when needed).