I think the better Way is to power the FT232R by the USB Port.
So the FT.. can always be initialized by the PC.
When you power the FT232 by your internal Power supply it can only work if this power is present.
The next Problem - Boncuk has described that already - is the possibility of ground loops.
When your device is connected to the PC and that device has Connections to other components that are conected to the PC, it is possible that the GND is tied together through the whole system.
At measurement equipment it is possible to get wrong results, or damaging of some parts.
I've made that experience with my LiPo Volt Meter.
There was a Charger with RS232 and the LiPo Voltmeter with USB both connected to the PC. First there would be shown wrong results. Then the A/D Converter of LiPo Voltmeter was blown. After installation of optocouplers the problem was solved.
When such one is planned in your case, you should use optocouplers to get galvanic isolation. The easyest place to do that, is at the TxD and RxD Connections between the FT232R an the rest of the circuit.
So the FT232 would be powered by USB and the circuit behind the optocouples has it's own power supply.
To create an USB by software in an tiny AVR like ATMEGA88 isn't an good idea.
Nearly the whole capacity would be used for serve the USB Port.
When you want to do that you'll better use an AVR with USP capability like the AT90USBxxx controllers.