Prompted by dr_andus' comment "fairly minimal," and by re-reading the OP, I think you may be less concerned by the total feature set, than by features not getting in your way. In which case, I suggest taking a look at the sticky notes program I use myself, the little-known
Magic Notes. From your point of view, the plus point would be that a left double-click on the tray icon (or a hotkey) gets you a new plain sticky note, with no fluff, with whatever defaults you've set. You can get to fonts, colours, alarms, attach-to-window etc., if you want them, by clicking the Note Window Menu icon or by function keys. But they won't bother you if you don't bother them. Right-click on the tray icon gets you About, Help, Preferences and other general program stuff.
Magic Notes is $19.95 payware. There's no generally-available free version that I know of, but the trial period is a generous 45 days. Development is glacially slow, but I've used it for years in different versions and it has always worked perfectly well. Its feature set is comparable with Stickies and Notezilla (the latter has more features, I think).
Another sticky notes program that I haven't tried, but which has been around for a long time (since 1998, apparently), is
TurboNote. TurboNote+ is on version 7.0. Its basic price is $US 29.97, but TurboNote v.3.4 is freeware (see their FAQ page).