When you add any new device to any external or internal port in Windows, the first time it's installed it detects the devices and installs the drivers. There will be a delay there. This holds true regardless of the file system on the drive, because the file system has absolutely nothing to do with the drivers being loaded. This is an issue with the controller drivers being loaded, something that is completely and totally file system and interface independent.
The next time, provided it's plugged into the exact same port, the loading will be almost instantaneous, regardless of whether it's eSATA or USB 2.
It doesn't matter if it's FAT, NTFS or CDFS, autorun.inf or no autorun.inf, if autorun is enabled in Windows, a menu will pop up, even if it's just to say "open folder to view files". If it doesn't, MS offers a tool on their website to fix this feature.
There exists no drive on the market that I know of that is capable of saturating a USB 2.0 bus continuous. It is conceivable that could change in the near future. The sole exception may be transfers of very large, contiguous files.
USB 2.0 can easily power a 2.5" drive. On the rare exception that it can't, the USB cable will have two plugs on it to plug into two USB ports for the extra power. 3.5" drive results vary. Typically they need a power adapter.
eSATA can not power an external drive.
Most external enclosures will offer both USB 2 and eSATA if they offer eSATA connectivity. Thus, it's not an issue if you choose to use the eSATA capability on one computer, USB 2 on the other.
The portable drive can be completely blank and Windows will still autodetect it and install the drivers. The exception is Windows 98. However, the manufacturer provides a driver disk for the rare occasion that a person is using a Windows 98 computer. The same holds true for USB thumbdrives.