First thing you need to work out is why is it hanging, before blaming it on power. On thing that may cause hanging is if when installing the, in the case of installing with a USB flash drive, is that the flash drive maybe detected as sda and the 64GB as sdb. But when booting the ssd then becomes sda and depending on how the kernel is told which partition is root you may have issues. Passing a UUID as the root partition will be more reliable than passing something such as /dev/sda1 or whatever. The device node can change depending on the order in which devices are detetcted and/or how many are plugged in, a UUID is pretty solid.
Are you not getting a grub menu ? Or are you getting a grub menu then a hang ? Or it could be a kernel config issue, the USB infrastructure is not available when coming to mount the root partition.
In the case of writing an image, are you using a x86_64/amd64 image and not an arm image ? This has happened, could be the Pi moniker that leads some to try and use a raspberry pi image.
As for the PSU, first you'll want to work the current draw is. If it's only drawing a maximum of 1.5A a 3A power supply will still only supply the needed current. If it is close to the 2.5A figure then there may be a benefit in using a higher current PSU; regulation & ripple can get a bit iffy the closer you get to the maximum figure. This of course will depend on design & build quality.
What you want is a quality PSU with good regulation and low ripple. And wires that can supply the required current without significant voltage drop.
Of course a PSU rated at 3A should deal with heat better when 2A is being drawn than a 2.5A PSU. But then again this will still fall back to design & build quality.