Sounds you have the background to be successful. Now you need to start collecting the equipment.
The first thing you need is something to act as a workspace. The best would be a laminar flow hood, but an aquarium on its side will do. You'll also need a pressure cooker to sterilize the growing media. Then you'll need varius peices tweezers and scalples. A scale is helpful too. Oh! and a pH meter (very important)
Whats really nice is that you can buy just-add-water orchid media. Most of them are pH adjusted too.
Once you have all the above, it comes down to technique. Sloppy technique will result in high contamination.
You can start making crossed now while you amass your lab supplies, as the capsules will take a few months to mature.
Also involved is a fair amount of research. Different genera like different pH. Paphs seeds hate banana, but the seedlings like it. Coconut water is loved by all. Knowing germination times is nice too. Phal take 2 weeks, phrags 6, paphs 6 (I think ) Stanhopea one day.
About not having a greenhouse, that is a problem. The potential is to end up with a lot of seedlings. You need to figure out what to do with them.
When deciding what to start with, consider how long it is to flower. Phals can flower a year and a half from flask, Maudie paphs 2 years. Cattleyas 6 years. I think Vandas a a long time too. Near blooming sized plants are easier to unload/sell/give away then seedlings 4 years from flower.
Good luck!