An RX 550 is an entry-level card, and doesn't need much power. Since it's newer and more efficient, it actually should have lower power requirements than the GTX 650 already in the system. The GTX 650 has a 64 watt TDP, while the RX 550 only has a 50 watt TDP, so if the power supply is enough for the GTX 650, it will most likely be enough for the RX 550 as well. Another option in a similar performance range to the RX 550 would be the Nvidia GT 1030 2GB, which is a bit more efficient still, with only a 30 watt TDP, and should perform similar to an RX 550 in most games.
However, it should be noted that while an RX 550 or GT 1030 should be a bit faster than a GTX 650, it probably won't be a huge amount faster in most titles, and if you are looking to give the system significantly more gaming performance, you would likely want something more powerful.
The 280X is in a higher performance class, though it is an older design, so it's a lot more power hungry, and can draw over 200 watts from the PSU under load, so you would likely want at least a good 500 watt PSU for one of those.
A GTX 1050 or 1050 Ti won't be quite as fast as a 280X, though it would still be a big step over the RX 550 and GT 1030 in terms of performance. And the GTX 1050/1050 Ti only draws around 70 watts under load, so there would only be a very slight increase in power draw over the 650, and therefore a good likelihood that the existing PSU would be enough for one of those as well.