This is a fascinating goal, and very difficult. It would make a book on recreating the history of science.
It took many people spending lifetimes collecting data to get anywhere. However, you don't need to rediscover that the planets go around the Sun I would think.
There are some key milestones that need to be reached. For example, you can distances to planet orbits in terms of ratios of a reference distance, like the Earth Sun distance, WITHOUT knowing the actual Earth-Sun distance. You only know that Mars' orbit is x times bigger than Earth-Sun orbit.
The first calculation of Earth-Moon distance was done by the Greeks. Aristarchus or Eratosthenes perhaps. One of them found the diameter of the Earth using shadows of monuments and in wells at noon, and the other estimated the arc of the Earth by Its shadow on the Moon, and thus the size of the Moon.
I think then it goes something like Newton measure the mass of the Earth by measuring g for a dropped object. Then using estimates of the Moon's distance and its orbital period he could determine the constant G in his law of universal gravitation. Then you can calculate the Earth-Sun distance and the rest of the planets fall into place based on their periods.
Now the other challenge is collecting useful data for determining orbits of planets. There are a couple of ways to "determine an orbit from observations". And this is a particularly useful project. Getting a mental picture of what to do can be difficult. But basically, you record the time and the position of a planet in some Earth centered coordinate system, like Right Ascension and Declination. Or relative to the know position of nearby stars.
Now, the orbits are ellipses with the Sun at one focus, so the Earth based system is not much good. You convert all your observations to Sun centered coordinates in the form of lines or vectors that point to the planet. But they point to the Planet from where the Earth was when you took the measurements. These are a set of lines in space and they don't go through the Sun or anything like that. They are just from some point in space (where the Earth was) pointing to the Planet.
C.F. Gauss (I think Laplace improved on this - not sure) showed that you only need three observations to find an orbit because only one ellipse will have points on the three or more lines and have a focus at the Sun. Two points are enough if you have other information like is it getting closer or further and which way is it going (it might be in retrograde so you can't tell).
More measurements taken further apart will increase accuracy and refine the orbit.
Also, the distance to Jupiter or Saturn could be found by watching their moon's orbits and noticing how they stray from prediction with distance due to the speed of light at opposition versus being further away.
So, you can see that the steps are not too daunting if you don't need to wait for a lunar eclipse and take a few other things as known.
I think you could do the temperatures with a small reflecting telescope. It is by detecting the infra-red radiation from the planet. A reflector is used so as not to absorb the IR. The instruments used were a bolometer that responds to heat and a galvanometer. The galvanometer is an incredible precise and sensitive instrument with no electronics.
Search on "calculate orbits from observations" and there are bunch of PDFs from good sources.