@toxicity4k, welcome to the forum.
The GTX 1050 Ti should fit into your case without any problems. You can be certain by measuring from the Back I/O ports to the front of the case. The specs for the card state that it requires a 300W power supply unit (PSU). Therefore, you may not have to upgrade the PSU in the computer since the current PSU is 460W. If you find that you still want to upgrade the PSU there should be no problem with one that is 600W. Again, measure the current PSU and compare the measurements to the one that you want to buy.
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I am not an HP Employee!!Intelligence is God given. Wisdom is the sum of our mistakes!!