I'll do a quick summary and then point you to a link with more detail.
1. Pot size: That's up to you. You can root-prune (and top-prune) citrus as needed to keep them in the same size pot indefinitely. But a larger pot means a larger plant and more potential fruit. So I recommend letting your citrus grow into the largest pot you can manage and have room for in your greenhouse.
2. Potting Mix: Wet feet = root rot = dead citrus. You want a potting mix that drains well. If you can't find a citrus mix, use a cactus mix. Or add coarse perlite and sand to an all-purpose potting mix.
3. Up-potting & root pruning: Just like any plant, watch for signs that the plant is getting root bound to decide when to re-pot. (Citrus don't mind being a little rootbound, but it gets hard to keep them watered when their pot is full of roots with almost no soil.)
If you want to keep the plant in the same size pot, cut off about 1/3 of the root mass by pruning it evenly along the bottom and all sides. Then re-pot in the same pot, adding citrus potting mix to fill the space you made by reducing the size of the root ball. Water well. You can keep a citrus in the same size pot indefinitely using this method.
4. Top-pruning: When you root prune (or just re-pot) is a good time to look for dead wood and crossing branches and trim those out. You can also lightly shape the plant to keep it from getting too heavy on one side, and prune it to keep it in its greenhouse space. But citrus resents heavy pruning, so don't cut it back hard unless absolutely necessary.
5. Feeding: Get a citrus food (palm food or fruit tree food also works, but neither is ideal) and feed according to package directions. Generally you will feed in spring when the plant starts to break its winter dormancy, in early summer, and again in August.
If the plant will be in a cool greenhouse over winter, you want it dormant over the winter. So don't feed after August or before February, as feeding encourages tender new growth.
But if the citrus is in a warm house over winter, you can feed it year round.
6. Watering: Keeping citrus constantly wet or sitting in water is the most common way that people kill potted citrus. Citrus is native to rainy climates with sandy soils. So it's adapted to a soak/dry/soak cycle. Allow it to dry out somewhat between waterings, but don't let it get bone-dry and don't let it get to the point of wilting. (It can defoliate or die if it wilts badly.) Water it well, let drain, then let it dry out again before the next watering again.
DO NOT LEAVE THE PLANT IN STANDING WATER. How often you have to water this will vary based on your potting mix, the size of your plant relative to its pot, temperature, humidity, and fruit load. In most cases you'll water 1-2 times a week, but if the plant is getting rootbound it may need water almost every day.
7. Temperature/Climate: Citrus loves sun, heat (well, maybe not Death Valley heat), and humidity. Citrus loves to be outside in the summer to soak up those rays! Just be careful not to let it get too dry - pots can dry out fast in the heat. You might want to acclimate the plant gradually to the sun over several days when you set it outside in the spring, especially if your citrus has been inside the house. Don't take it outside until danger of frost is past.
In fall, bring it in before the first frost. (Cool temperatures won't cause any harm - the plant will simply go dormant if it gets too cool. Just don't let it get frosted.)
In winter if humidity is very low, misting or using a humidity tray can be helpful, but again, do NOT leave the roots standing in water. You can set the pot in a tray to collect excess water - you can leave the pot in the tray so it works as a humidity tray IF you fill the tray with rocks and set the pot on the rocks. This keeps the base of the pot from sitting in the water at the bottom of the tray.
8. Growth: Citrus grows in flushes, several times a year. So your plant will sit there unchanging for weeks (or all winter if it's cool enough to stay dormant) and then POW! Buds will suddenly swell and growth will pop out everywhere. The plant can get much larger in just a couple of weeks. The process is so fast that you can almost sit there and watch it grow. Then nothing will happen again until the next flush. So as long as the leaves are a healthy green, don't worry if the plant doesn't appear to grow for quite a while.
Fruit is the exception, since once the fruit has set, it will grow steadily until it reaches full size. Then the fruit will hang there green for weeks or months before coloring up. You can't see it from the outside, but the fruit is maturing internally during that time.
9. Harvest: Any time after the fruit is fully colored. Except limes, which are usually harvested at the full-sized green stage - but as a homeowner, you might leave some to ripen - they will still taste limey but be sweeter. You might like them better harvested ripe.
Harvest time varies depending on the type of citrus. Many lemons and limes are everbearing - they will bloom several times a year, and fruit is ready usually about 9 months after bloom. Most oranges, tangerines, and grapefruit will bloom in spring and be ready harvest in fall or winter.
Most citrus will hang on the tree for 3-4 months after coloring up, and generally gets sweeter as it hangs. Sometimes it falls just before the next bloom, or when it is about to go bad. Though some fruit can stay on the tree even longer, but some Satsumas don't keep very long well on the tree and need to be picked within a month or two. You'll need to research the harvest time and tree storage time for your specific varieties.
Here are a couple of links to read more:
minnesotacitrustrees.com/citrus-care/repotting-citrus-trees/homeguides.sfgate.com/potted-citrus-tree-care-55379.html