All are supported, including Safari.
Every browsers has its pros and cons, most of the time the recommended browser is bound to company policies.
As an admin, personally I prefer Firefox. Using the Firebug add-on when needed to troubleshoot is very convenient. Granted IE has it's own "developer mode" now, but I more familiar with Firefox.
Various browsers are supported for PeopleTools. It depends what version of tools you are using and what version of browsers are supported for that particular tools version.
Those information can be obtained under the certification TAB. You can go through the following navigation.
Steps to check the certification
All the certification information can be checked on certification page
Here are the steps
1) click on certification TAB
2) Product:- PeopleSoft PeopleTools
3) Release :- 8.52
4) Click Search
It will give you all the following options and you have to choose according to your requirement
1) Operating System
2) Application Servers
4) Desktop application,Browsers and clients
5) Directory/LDAP Services
8)Management and development Tools
This document will let you know also if there are any issue related to particular browser version
PeopleTools 8.48 - 8.53 Browser Compatibility Guide (Doc ID 704492.1)