Well done mate on that Milky Way shot with the other camera, it's awesome in itself.
These are the settings I use on my Canon for wide field.
ISO 800, sometimes 1600 but I try and avoid this due to noise.
I use a "Cable release" and set the camera to fully Manual mode AND SWITCH OFF AUTO FOCUS on the lens. !!!
I would experiment with your aperture settings. In my case is stop it down 1 or even 2 steps to get better star points. Leaving it wide open you may get bloated stars.
But see how you go with your lens.
Focusing is a little tricky but not as bad in wide field shots say at 18mm but as you go through to 300mm focus will be critical.
At wide field I usually take it to infinity and back it off just a par sec or two
*you know what I mean* (just a touch).
Check it out in the viewfinder but it's not always acurate.
In deeper field shots ie 300mm I use a right angle finder and set it at x2.5 which gives a mag view of the star. I try and remember the best focus point and mentally set it each time but it's best to put a small mark for future focusing.
In your model I would set Noise reduction on and also MIRROR LOCKUP
Also I recommend the cable type remote not the wireless remote for astro because later you will need DSLR Focus or similar to control the cam via laptop.
The wireless control is great for family portraits but for astro I prefer cable control.
Hope it helps, I'll think about what else and post again.
BTW does the 350D have the old 300D style cable plug which is just a 2.5mm stereo plug or is it the proprietry 20D style 3 pin plug?