Many ICs are available to do this (Score 1)

Have a look at http://www.beyondlogic.org
They have very good sections on interfacing to a PC using USB.

I have used several USB ICs from Philips, and all are simple to use.

Points to consider
1) If you only want to support the slow USB 1.1 devices (1.5Mbps) then look at USB enabled Microchip PICs
2) Must of the ICs available are in packages that need to be surface mounted. Try buying a development board or evaluation kit, unless you are really good with a soldering iron.
3) USB devices have the idea of a class. e.g. if your project supports the "serial" class then you can use the USB serial driver in linux.
If you need more flexibility you will have to write a new driver to support yor custom device class.
The USB linux drivers are fairly mature and there is documentation on writing new USB device drivers.
4) There are four different USB transfer types.
Control (mandatory) / Interrupt / Bulk / Isochronous (regular transfer with reserved bandwidth)
Ensure the ICs you look at support the transfer types you need and have enough endpoints (channels) for your needs.