I probably wouldn't. Bike parts are much more expensive bought piecemeal than as an assembled bike, so upgradeitis, can be very costly, and highly questionable in financial terms.

You can maintain borderline financial sensibility by replacing-with-nicer as and when something breaks, but even then you don't want to climb too many steps on the quality ladder. If you can see already that there are a lot of parts needing attention, try keeping the bike rolling with a minimum investment while setting any "upgrade" money aside for a whole new bike instead.

Sometimes people determine that they've found the frame of their lives, which just happens to be decked out in poor parts. In such a love affair obviously "sense" goes out the window. Then it's just a matter of picking the parts that fits.

The main killer of inexpensive wheels is poor assembly. It might be sensible to have bearing adjustment and spoke tensions checked before the new wheel has seen too many miles.