I'd prefer the drill press for casework, but honestly if I didn't have a cordless drill yet I would buy one before I got a drill press (having both myself) even though it meant I was making that minor sacrifice in my audio work until I got a drill press someday.
I don't know that you need an expensive (as expensive as a drill press) cordless drill though, I find my 1/2" corded drill WAY more powerful than any cordless drill and would suggest a corded drill trumps a high-end cordless and can be bought with the $ difference between high-end and fair quality cordless drill. It might be a bit different if you were doing construction work and needed to drill concrete or 2 dozen floorboards or whatever on a remote job site but for casework alone I just wouldn't buy an expensive cordless drill, especially just starting out on a tool collection and having held out without one until now.
I'd tend to think a "good" drill press is a few times more expensive than a good cordless drill too, $100 Delta is a good buy but more what I would call entry-level, mininal acceptible quality for more precision-oriented work rather than seeing it as "good" vs a really horrible one being "bad" as most of the rest in the sub $120 range are relatively low quality, low end. "Good" might be considered $500 and up range, though it's generally a larger press than casework needs.
The Delta 10" looks like a great value for it's size, but a bit underpowered for the jobs you'd do with a larger drill press. It's large enough for this kind of work but consider that some drill presses last decades, are handed down to your children years from now while a cordless drill is all but dead from battery failure in 10 years - less time if you use it regularly, and after that much use it may not make sense to buy a pair of new battery packs, depending what kind of jobs you were doing, the wear on it.
I suppose I'm suggesting that, supposing something like a $160 budget, and having neither of these yet, I'd get the $100 Delta press and a $60 cordless drill. I wouldn't bother getting a much cheaper drill press though, since I suspect you are young not having a cordless drill yet and that means you (hopefully) have a long life ahead of you and more $ spent on a drill press might benefit you for half a century rather than single-digit # of years. Because of that, if you see yourself doing anything more than casework with your drill press, I'd budget a few hundred $ at least.