Agree with what others said, put your legacy pets on hold for now, until you have a better sense of the current game and the pet system. Don't sell or trade them off, for now, or ever, since they aren't replaceable and you're coming into the UO economy of today. I'll try to give a brief and helpful run down to help get you going and enjoying UO again.
Getting the mastery book. If you don't find one on a vendor, you can run the mastery quest for peacemaking for as many as you want. Go to the bard school in Britain. Very easy way to get books. You can also get a book through Hawkwind at the gate to Eodon, one of the moongate destinations, but it will randomly generate a quest that's not easy.
Taming and training a pet for learning the system. For rideables, I would recommend Cu Sidhe as top tier, then Firesteed as second tier. The advantage of Cu Sidhe is self-healing. Also, you can get overcapped energy resist. The ideal Cu resists are 70 Cold, and 85 Energy. The rest can be set after training. Opinions vary on the resist thing, which could flare up for some. For Firesteed, the advantage is being able to specify 2 special moves. For a general adventuring pet resist, try 80/80/60/65/80, the reason being physical is the most common monster attack damage, while fire and energy are the most damaging caster attack damage. Cold is extremely uncommon as a damage type. Tame a few of the pet you want to try, feed them, and then stable them for a week until they bond. You bond them by feeding them. Feed, stable, wait a week, feed again, and you should get the "bonded" message.
The nightmares that spawn now have a rare type that spawns very rarely, so you have to farm them in Ilshenar. 2 slot Void color is the one to get, but you can use the other rare 2 slots to experiment and try things out. Don't forget you can move a character over to the test system and try it there to make sure it's the set up you want. For my preference, I kill off the nightmares with a 3 slot pet. This also prevents you from taming a 3 slot rare, which will end up with a lot fewer total skill points because it is missing the chance to move up one level. Nightmares are nice pets, but like most people, you might find that for whatever reason, you rarely hunt with them. One advantage they have is the ability to create a "Necromare". This is a mid/advanced pet to create with really tight points on current spawn, but it's worth doing, in order to try it.
Pet training and skills. You can get a nice pet using 105 and 110 scrolls. You can get these by doing treasure maps. It's not documented on UO Cah, but you can get 110 Wrestling this way too. Getting maps, you can do from fishing or from farming monsters that drop certain maps. It needs to be done in Fel, to get Fel maps since these are the only ones that will give scrolls.
Are you on other shards or Siege?
That link is great, I marked a rune to the crazed mage and plan to give a dragon a workout later. You say they may be worth a great deal, could you explain how?
