if you need DC and 1mA resolution then good luck with that, you're probably an order of magnitude off in your price expectations for anything other than getting lucky on a 25+ year old tektronix probe from ebay (and by lucky i mean in both the auction and in getting a working unit, as known good probe+amplifier combos normally go for more than your budget so you'll be rolling the dice on "as-is" units). AC probes like those suggested above are cheaper - also look for 1V/A "Current Monitors" from Pearson, but they'll still be a few hundred bucks unless you're lucky.
DIY wise, if AC is ok and you don't have wide bandwidth requirements (e.g. if you need up to 200kHz+ but only down to say 20kHz), and don't need a clamp-on solution, you can probably DIY a probe for $10. DC you might scrape by with a LEM current sensor or something - they are normally specced to about 200kHz and a low-range unit might just get you 1mA resolution, though again with no option for clamp-on.