If you use the Hardware USART you MUST use an hardware inverter, either a MAX232 or equivallent, or just a simple transistor as an invertor. You cannot invert the USART through a software setting.

Only SOFTWARE asynchronous communication options such as DEBUG, DEBUGIN, SERIN, SEROUT, SERIN2 and SEROUT2 give you the ability to invert. You can connect then as per the diagrams in your PICBasic manual using just a simple series Resistor. I have used values as low as 1K5 without doing any harm to the PIC.

If you are new, start with software and work you way up to the Hardware after you feel more comfortable. In the code examples section is a ready-to-run application "Communications Example : PC to PIC bi-directional dialogue" just change the ports and settings for your preferred PIC, Port and Pins.