Use wires as much as possible
For instance, don't broadcast television over the air, but instead use cable exclusively. Don't use wi-fi, just wired ethernet. No cell phones, just "landlines".
Big sources of electrical power will give off detectable signals. Shielding these isn't hard, however: A simple conductive, grounded shell around it will easily block the wayward signals.
Do the same for electrical and data transmission lines as well; not only will this improve your signal integrity anyway, but it will prevent leaking signals beyond the physical wires.
Your buildings should likewise be shielded to block any wayward signals. For extra protection, build underground to get the added protection of the ground itself.
When wireless communication is required, use as little power as possible
A walkie-talkie is handy for communicating over open distances of up to a couple of miles, but isn't going to be detectable from orbit, let alone out in deep space -- it's just too weak of a signal to stand out against the background noise.
You can further reduce the risk of detection by using directional transmitters, such as lasers and microwave transmitters, especially for those times when you just need to boost the power to get a signal to go farther.
There's lots of background noise in space, across every possible frequency and spectrum. When looking for signals from intelligent sources, then, the key is to look for patterns, and discard all the rest.
Enter encryption: A good encryption algorithm produces output that, ostensibly, is indistinguishable from randomness. You can't look at a block of such data and determine whether it is the works of William Shakespeare (encrypted), or just a whole bunch of random 1s and 0s.
Modern communications protocols require some non-encrypted header stuff, but if you were to mandate that everything that goes "on the wire" is always encrypted with, say, AES-256 using the common password "P@s5w0rd!", everyone can still decrypt and read it (notwithstanding additional encryption that might be being used for actual privacy) but the very nature of it being communication has now been effectively obfuscated.
Now, you'll of course have to modify or invent something new to encrypt not just digital 1s and 0s but also the analog carrier signals used as well, lest you produce the recognizable pattern of "highs" and "lows" that betray the use of digital technology, but that's pretty much just window dressing.
Encryption is not a panacea, however -- you will still have to rely as little as possible on wireless signals, and use as low power as possible, to minimize the risk of detection. Encryption just adds a little extra protection when you do need to use them.
Change frequencies regularly
At the same time, you'll want to avoid relying on certain frequencies too much, as even if it's unrecognizable the spike in certain frequencies can still betray you. This can be accomplished by using a variety of different frequencies for all methods of wireless communication, mixing the use of radio and microwave, and even using combinations thereof for the transmission of individual signals/messages. The result will be a very complicated communications infrastructure, but given the risk if you're discovered the complication is worth it.
Make your satellites rely heavily on optics
Signals from your satellites should use directional microwave; being aimed at the planet, there's very little risk of detection from beyond it, and what little does leak out will look like random noise thanks to the encryption you're using.
Sending data to your satellites is a bit trickier. It's hard to aim carefully at something a hundred or so kilometers straight up, and moving fast, and not accidentally send your signal into deep space where you risk revealing yourself.
So instead, equip your satellites with telescopes and have them aim at ground-based pads. These pads, using whatever technology you want, would produce optical patterns to communicate data (think those QR codes you see everywhere). Your pads should be able to quickly change their patterns to communicate new data, of course. You could even just use blinking lights. Detecting such a method of communication would be impossible for anyone who isn't already looking directly at your planet -- at which point they'll simply see your colony, your satellites, and secrecy is straight out the window anyway!
Stopping bad actors
To maintain the requirement that ships can come and go unimpeded, you can't shield the entire planet. (Besides, even if you say cost is no object, that's a monumentally costly construction project, not just in terms of money but in logistics and time as well.) The only way to stop someone maliciously transmitting from your planet and giving you away is strict internal security: Nobody but authorized personnel is permitted transmitters of any variety, for instance, monitored by heavy surveillance and enforced by harsh penalties. (Surveillance need not mean video cameras everywhere and your version of the NSA reading everybody's emails; since it's rogue transmissions you're worried about, simply detecting unauthorized transmitters -- which can be done with passive sensors -- is sufficient for this purpose. Up to you if you want the cameras and NSA in addition, though.)
You should also equip your satellites with precision orbit-to-surface weaponry. Whether that's lasers or kinetic weapons depends on available technology and your preferences, but the idea is to monitor for any unauthorized transmissions that could even remotely be detected from space, and quickly vaporize the source.
Working in your favor is the fact that even a high-powered transmission has to remain on for some time before anyone beyond your system can detect it, let alone identify with any accuracy the source. Your orbital weapons are more than responsive enough to deal with this threat.
This even assumes that we're dealing with highly advanced communications technology capable of far-faster-than-light communications. If you're limited to the types of communications we know of today, then you really just don't have anything to worry about, as it would take decades for the signal to reach even your nearest neighbor, and odds are that one's not inhabited anyway.
All this being said, nothing you can do can prevent someone on one of these ships that's coming and going from reporting your location to the authorities after they've left, so if bad actors is your threat you're pretty much hosed without blocking everyone from ever leaving your planet again.