Ultimately it all comes down to how comfortable you feel and how quickly your body adapts. It is an individual thing.

In regards to depth: Simply go as far as you can before you start to gag. Over time you will probably be able to put whatever you use to train in deeper before it becomes too uncomfortable.
You may simply have to test that.

The toothbrush is a good start. Alternatively to the toothbrush many people suggest opening your mouth as wide as possible - as if you are yawning - and then stick a finger in there as deep as you can.

Some people recommend moving up to a (peeled!) banana: It has the upside that it's soft, curved and size-wise closer to a dick. Once you can swallow that, you can move on to a dildo if you need to. Make sure that the dildo is on the softer side, because hard dildos can get you a sore throat.

Take your time with this, but keep at it. Most people do it once per day. Once again, it varies how long it takes, so don't feel frustrated iftakes a while before you will be comfortable with it.

I haven't tried this, but you could probably do condoms over carrots or cucumbers. They come in a variety of sizes and you can use a peeler to shrink the carrot if it's too big. Maybe even skip the condom to avoid risk of swallowing the condom. Banana sounds like a really good idea.