Upgrading my dell 4550

No, your 250W psu will not power this card.

I can't tell you whether the Dell 4550 uses a standard ATX power supply. If it does, you need nothing else - your new vid card uses 2x4pin Molex connectors for extra power, and your new psu will have them. If it doesn't, then you really cannot upgrade. You can try the Dell User forums or maybe Dell support to find out.

The vid card may be difficult to install. There may not be enough room in your case . . . an air duct or something else may block the end of the motherboard.

Be careful pouring money into upgrading this Dell. You know you are pushing the limits of a defunct technology, and you are doing it in a box not designed for upgrades. They give you systems, often at a low cost; in return they want you to buy new rather than upgrade.