[Out of character details are in square brackets and red instead of white]
First, I’d highly recommend you read the Markann’s notes on magic [also look at spell-casting ]. Look at the books we bought to see all the different spell colleges and spells you can use [GURPS Magic]. Some higher tech spells are not in those books, though, such as the genetic-engineering spells I used to replicate the Markann’s research [which were based on spells in the GURPS Bio-Tech book].
Since you now know Thaumaturgy, you have a key prerequisite to be able to cast new spells. Look at the rules for modifying spells using spell modifiers. The ability to modify spells makes magic much more powerful. For example, the standard spells only allow you to learn a skill temporarily from willing subjects, but I was able to modify the Borrow Skill [Magic, p. 47] spell to learn genetic engineering from the dead Markann permanently. [The Cosmic and Retention spell modifiers were used. The Cosmic spell modifier is indicated in Basic, p. 103, the “ability other than an attack or defense” version. This modifier is especially useful: it removes limitations in spells. In this example of Borrow Skill, I had to remove the “willing subjects” limitations to learn from the dead, and thus needed to use Cosmic twice – once for “willing” and once for “subjects”.] The party’s mages have now cast a variety of modified spells.
I recommend figuring out what spell you would like to know, and then figuring out how to get the prereqs necessary to achieve that. (Although if you just want to cast a spell for an hour, you can use your Wild Talent without knowing the prereqs. I’ve done that a number of times.) Looking at a chart of spell prereqs helps you to figure this out quickly [GURPS Magic – Spell Charts (separate book than GURPS Magic)]. With my background, I’ve been naturally concentrating on spells in the Communicating & Empathy College, though I will start broadening my spells soon. In retrospect, despite not knowing thaumaturgy, Benolaa somehow seemed to be intuitively learning the spells necessary to start enchanting objects.
Happy: it sounds like you want to work on infusing high-tech items with magical properties. I think you’ll be able to create a lot of very cool and unique items this way. You’ll want to learn Enchant [M56], Power [M57], and probably look at Technology Spells [M175]. Also, you’ll be able to create items faster if you know Recover Energy [M89] to be able to rid yourself of fatigue quickly (depending on your IQ and Magery ability).
Lazarus: with your ability to seemingly know whatever skill you want, you could take your mage abilities in many powerful directions. You might want to consider learning Ensorcel [M60] to cast permanent spells on yourself. Doing so could give you powerful abilities, especially combined with your abilities to teleport and shape shift.
[We have an excellent GM that likes and encourages us to use the rules he set up in innovative ways — even if they’re extreme, such as learning from the dead or making incredible wealth. Take advantage of it and create interesting and unusual spells and equipment. If you have questions or need assistance, ask him (I’m always happy to volunteer our GM). He gave me substantial help in figuring out how to do what Quesix wanted to do!]