Noise sources by frequency (by no means exhaustive):
50-60Hz, harmonics: power line, electrostatic in nature
10-100kHz: lighting, some switching supplies, phase controllers (especially if repeating every 100-120Hz)
500-1700kHz: AM broadcast (do you live within a few miles of a commercial antenna?)
2-80MHz: shouldn't be much, but includes nearby shortwave or VHF / TV transmitters, or poorly behaved switching supplies (don't buy direct from China, amirite?); ESD transients may also pop up randomly around here (e.g. shifting in your chair)
88-108MHz: FM broadcast (do you live within a few miles of a commercial antenna?)
>110MHz: aviation (110-130), military (200-300??), UHF TV (various up to 700MHz?), etc.
You'll still be able to observe signals beyond 100MHz, the scope isn't a brick wall -- the amplitude won't be accurate, and the wave shape will be severely rounded (it's not picking up most or any of the harmonics). That high frequency junk you were picking up looks like it might be a pair of nearby FM transmitters, triggered in such a way that it produces a stable display (showing the point time where the two different frequencies superimpose constructively).
Common mode chokes (one or more turns through a ferrite ring or clamp-on) are handy from time to time, but taking some time to understand the nature of the noise is important. In your case, the high frequency noise is picked up when the "probe" acts as a loop antenna, and goes away in close proximity to the ground plane (working over aluminum foil isn't a bad idea, given that it's a bit of a short-circuit hazard!). At least, if I understand your pictures correctly.
For your development application, you'll have best results with totally shielded connections -- don't just hang a BNC on twisted pair for example, that's a good antenna in the millivolts! It has to be coaxial into circuit ground, shielded as hard as possible. Even an "edge launch" configuration (like
here) is noticeably more susceptible than a fully shielded enclosure.
As for your circuit's actual resistance to such influences: do take every opportunity to apply ESD and EMC protection and filtering to exposed connections! Only use the bandwidth you require. If your amplifier is covering more frequencies than you need, you will *see* more frequencies than you need!
Tim