You can produce your own hybrid and even give it a registered name but first you have to do a little bit of research.
Does your first Phal Hybrid have a name? If so, you can look up the RHS Register of Orchid Hybrids to see if has been used to produce hybrids. Some hybrids have been extensively used because they produce good "Children" others have proven to be infertile.
Of course, you can cross a NOID with another NOID and maybe you will get good results, but the progeny will all be NOIDs.
There is the time factor, no idea for Phals. For Tolumnia hybrids it is a 4 to 5 year wait till you see the first bloom.
How many flasks will you get? No idea for Phals, but for one Tolumnia cross received 8 flasks back from the lab.
That is enough for now! Did you intend doing the flasking yourself?

Here is a link that might be useful: RHS Orchid Database

I hope I haven't made this sound all too hard.....the great orchid hybrid makers must have made a start somewhere.

Thanks for the advice!

From pollinating a phalaenopsis to blooming the first flowers may take four to five years. The seed capsule takes six months to mature. The flasking operation can take 12 to 18 months before they are ready to be planted in a pot where it can take up to two years (or more depending on your growing conditions) before it flowers. The flasking operation is complicated and time consuming. Growing baby plants (seedlings) is also difficult.

I would recommend that you practice your growing techniques before you dive into flasking and breeding.

Matt

Matt could not be more right. It is difficult and takes specialized equipment. It's not as simple as planting some seeds and watching them grow. Sterile culture is involved. Look up the term both Arthr and Matt used: flasking. As a beginner I also urge you to focus first on learning how to grow the plants. Without that you'd never get the babies to grow.

After a few years when you know you can grow and rebloom them, then you can think about attempting the process. During the time definitely educate yourself on the flasking process. Buy some compots and grow them up. Buy a flask and try to grow it up.

Basically, your best bet at success is to build up to doing it all on your own, which I assume is your goal. Arthur's advice is also priceless (though I might be putting words in his mouth): go ahead and pollinate your plants. Get that experience. There are also labs that will grow the seeds for you. Lots of ways to go about this!

Thank you, I'll definitely do that