Sam, What is your Milling machine? There is a big difference in rigidity between machines and in particular the rigidity of the column. I myself refer carbide cutters now days. Out here in NZ they are about the same price as HSS if they are 10mm and smaller and last a whole lot longer. Being as you are on a manual mill, the carbide will work very well. I don't think carbide cutters come in screw shank for Clarkson type holders though. All that aside, with you making the T nut exercise, in mild steel, 600 rpm seems about right. Depth of cut could well be on 0.5mm on your mill per pass if it is not rigid enough. If your machine has ball screws, that makes it very easy to climb mill. But a non ball screw mill, you are best to be conventional milling. If you can't make the pass in 1 go, ie you have a 12mm cutter and the part is 14mm wide, I would be cutting at just over 7mm wide pass each way at what ever cut depth that did not labour or load the machine too much. Coolant or one of those air misters that will blow the chips away from the cutting surface and cutter flutes as well. Milling on a manual mill in the home workshop is no where near the speed or feed of a substantial cnc machine. The Gibs on the X,Y,Z really need to be correct, ie there is slop in them. The gib lock or slide lock should take very little to create resistance on that slide. When we used to use old worn out bridgeport mills, we used to lock the axis we were not using, and the axis we were using used to just sinch up that axis, so it could be turned ok with a slight drag. Even with carbide cutters on your home mill, you probably will still use similar speeds and feeds and the cutters will last you 5 times longer over your HSS. Try using a smaller cutter like an 8mm or 10mm diameter cutter. They will put less load on your mill and are slightly cheaper as well.
The formula I use is (318.3 X cutting speed of material )/ diameter of cutter or work piece. For mild steel I use 25m/min eg (318.3X25)/12=663 So choose the closest to it, but I would not run 700 rpm , I would run slower with HSS cutter. Feed rate is from 0.03 to 0.1 mm per rev per tooth. In softer materials like free cutting MS the feed rate can go to 0.2mm per tooth, but the depth of cut is limited to how solid your machine is. If you are cutting harder / stronger materials, the cutting surface speeds go down and you may need a lower depth of cut. I suggest at 0.5mm depth and if all is good keep going deeper until it sounds loaded or as you have described, starts to really shake and rattle. There is no point in taking big cuts and wrecking the machine.
Neil