Don't bother. The USB ports on the PS2 are USB 1.1 rendering transfer speeds slow and making compatibility poor and even if they do work slower speeds than just from disk (FMV's choppy, slow loading etc...)
If you really want to connect up a HDD look into HDCombo or HDConnect
Since you have a slim i recommend loading via network. It's noticable faster than loading from usb, but still slower that disc or HDD.
I think the speeds are about the following:
usb: theoretical max speed 1.1 MB/s
LAN: should actually be 1-2 MB/s
disc: up to 4x dvd = ~ 5.5 MB/s(the more the data is away from the middle of the disc, the closer it gets to that speed)
HDD: depending on the HDD, but should always be faster than disc
As loader i recommend Open PS2 Loader, it does USB, LAN and HDD loading, and is still in development, unlike USB Advance and HD Loader.
Initially you at least need a disc version of uLaunchELF. You can (and need) to burn one yourself.
For rest I am not sure, All I can say how it essentially goes on PS2 side is that you need also a USB stick with the needed ".elf" file. But on PC side to send the games, i am totally uncapable of saying anything on it, as I have not tested at all.