If you want to dabble for _cheap_ with SDR, the RTL-SDR [1] is a < $10 USB receiver that works from 24 to 1766 MHz.
It allows to listen to FM radio, decode most 433MHz devices (weather stations), car keys signals, and even NOAA weather satellites [2] with a DIY antenna [3].
You can also track your neighbors' energy usage by decoding their smart meter transmissions (around here, they transmit about every minute). https://github.com/bemasher/rtlamr
I can read about 40 smart meters from inside my home using the antenna that comes with it.
Said from experience of having built something more complicated and having it perform worse than two pieces of copper tubing stuck in a piece of scrap plastic.
I've been dabbling with RF, but I don't quite understanding the appeal of downloading NOAA sat images. It is simply 'hello world' for receiving sat downlinks?
For me it's a "hello world" for experimenting with building VHF antennas. It's nice, because they are on a schedule that you can plan around and more interesting than listening to the local dispatch systems.
As an aviation enthusiast, I've got a Raspberry Pi in my attic hooked up to two RTL-SDR radios, each connected to homemade antennas mounted on my roof (one VHF to listen to airband transmissions and the other receiving ADS-B[1]). No signal processing required--both are pretty easily achieved by just cobbling together existing open source packages. Also have a GPS receiver on the roof so that Raspberry Pi is also a stratum-1 NTP time server[2]. But that one's not using an SDR. Fun hobby.
EDIT: Added links I found helpful, for the curious:
Can you suggest something that could be used to read or reprogram wireless access cards, such as the HID Proxcard II? I want to clone my apartment's key fob into a bracelet I can wear when I go jogging.
Clarification for the audience: "RFID" has very little to do with radio or SDR. Communications are done with a coil in the "near field", which also powers the tag.
Not all RFID cards are created the same. Most RFID cards that are some kind of "smart" (i.e. contactless bank cards, subway tickets) conform to ISO/IEC 14443 standard that mandates the use of ~13.5MHz carrier to communicate between the reader and the card. This is "the NFC" as your phone understands it.
Proximity cards used for door access usually have the 125kHz carrier compatible with the EM-Marin EM4100. No cell phones I know of have an antenna for this frequency range; therefore, no phone can read, clone or emulate an EM-Marin proximity card.
Since the HID Proxcard II is a "value priced 125 kHz proximity card", you cannot use a phone to read it.
Assuming you could read signals to/from a key-fob/HID-card, isn't there some encryption involved that would prevent merely repeating the signal to "clone" a key-fob?
Nope, an EM4100-compatible card (or a key fob) is just a 64-bit ROM with radio interface. You can read its value and replay it to a reader; the latter won't be able to tell the difference between the original card and your spoofed one.
Better (and more expensive) RFID tags may have an encrypted communication protocol.
I can read about 40 smart meters from inside my home using the antenna that comes with it.