I am going to make an assumption, based on your technological constrains, there is no FTL of any kind, including travel, communications and emissions.
When you said "And the colony ship is on the outer reaches of the system, (~4-5 billion miles? can be any reasonable distance)" may be a little too small of a number. This places it equivalent to the orbit of Pluto. They would probably be making observations long before that, many of which they would actually make before leaving Earth.
Now, I will assume your distance of 5 billion KM for this. Your ship would be equipped with enough sensors to successfully detect a the needed resources to determine where to set up the colony. These sensors would include spectroscopy in many wavelengths ranging from low range radio waves through deep infrared, visible light, ultra violet, x-ray and gamma. They will have optical and radio telescopes. in 100 years or more, they may also be able to use particles, such as muons, bosons and MAYBE some exotic particles to assist in chemical analysis' of there target colony. They may even have some sort of rudimentary ability to use gravitational lensing to assist in detection or carry some ability to detect gravitational waves, assuming the technology was miniaturized enough at this.
These are a sort of passive form of analysis. They would need to position themselves so the target would lie between the star and themselves. That can take some time to get into an optimal position to allow for analysis. Less reliably, they may also have a small suite of active detection systems, such as LiDAR, RADAR or microwave sensors. At this distances, it will take light ~9.25 hours to make the round trip. It would be very difficult to make a good lock on your object at these distances and, due to various reasons, will take a very long time to gather enough data to overcome background noise.
Now, just because you have all these sensors, doesn't mean you can do anything with all this data you will be receiving. You will probably have very large banks of super computers, maybe even super quantum computers. Even with 100 years of technological advancements, it will take some time to gather enough data to analysis it to tell the difference between useful data and noise.
Now, for timing
Observations on certain wavelengths can be near instantaneous. Optical, radio and microwave observations (not active detection) will tell you what it looks like based off the energy it reflects from its star and what energy it produces and releases itself. Give it a little time for the super computer to analysis it over the wide wavelengths of observable light and you get a picture of what it looks like. This wont tell you much more than that.
Your active sensors can constantly bombard the object with energy from across the spectrum, but it will take >9 hours to get returns, and maybe several hours to several days to analysis the data. From this you may get more data about composition.
After making appropriate maneuvers, you can get this object aligned for your spectroscopy sensors to have a look. This can get a lot more data such as chemical composition, maybe structures below the surface and a better understanding of its mass and impact on the star itself. Then all that data then needs to get processed by the computers. This could take weeks to months to get in the right position.
To sum it up, immediately, you know there is something there, and its SCREAMING in radio frequencies, and probably also in x-ray. You probably already knew this prior to traveling. It would take days for your active sensor to look at it. It may also take days for the spectroscopy to analysis it as you should have know it was there and had long ago positioned your ship to look at it, once you were close enough to make observations.
