My 2 cents….
When selecting a turbo, as mentioned above definitely get one with a water cooled center section. If you can afford it, also get one that has ball bearings rather than a sleeve bearing. They last longer and you typically get the latest technology sinc turbo manufactures are putting most of their r&d into ball bearing turbo’s.
If you already know this then please disregard my comments. Making horsepower with a turbo is not a function of psi. Psi is essentially a measure of resistance. It’s all about volume of air flow. Not pressure. For example, turbo A might flow lets say 35 lb/min at 17 psi while turbo B might flow 50 lb/min at the same psi and at the same efficiency island. The difference in these turbo examples are typically their size and technology. Flow maps will show you the cfm at various psi for various efficiency levels. Try to match your turbo selection to the cfm (at a streetable psi) required to make your hp target. Then there’s lag to consider. As has been stated above the turbine housing size will affect lag. The smaller the a/r the quicker the spool up but at the same time a small a/r can restrict high rpm performance because of exhaust pressure. I’ve found that a small a/r turbine housing is difficult to drive because it has so much bottom end at the expense of the top end. It’s a matter of preference. I went from a T3 .63 a/r to a T4 .82 a/r. I didn’t notice much of a change in the bottom end but I did notice quite an improvement in the midrange and top end. Again it’s a matter of preference and driving style.
Also take into consideration the cfm flow of your head/cam. The cfm of your head and cam (that’s a whole other discussion) will give you a ball park of the max cfm your engine can move which in turn gives you an idea of the turbo cfm your engine can handle. Too big of a turbo and you’re adding more flow than your engine can handle thus creating flow resistance (unequal pressure before and after the turbine housing) while typically introducing increased turbo lag. Too little and you’re leaving hp on the table. Simply, it’s about the amount of cfm required to meet your hp goal, and whether or not your head/cam can flow those cfm numbers. Then select a turbo that makes that amount of cfm, at a streetable psi, at the sweet spot or close to the sweet spot of the turbo’s flow map. And lastly don’t forget to port your turbo exhaust manifold especially where runners 1-2-3-4 come together just before the exhaust flange.
The trick is to get everything to work together in balance. Good luck.