The annual "health check up" for healthy reptiles is a totally pointless and potentially costly exercise. Dogs and cats go to the vet annually mainly for their necessary vaccinations, and other general assessments - heart, teeth, coat, weight etc are made at the same time. Our reptiles don't have vaccinations, and any assessments of good health should be obvious to the owner/keeper as the animal progresses through its life. If you've got an interest in, but don't feel confident to make such an assessment yourself, try and find someone nearby who can check the animal out and have a yarn with you occasionally. If you have any questions generally, this place is a good source of helpful info, and you'll find that most respondents to your questions will give you good advice. The good thing about APS is that if a member offers crappy or dangerous advice, the grumpy old men like myself will dump on them from a great height :evil:, so the advice you get will be subject to scrutiny by very experienced eyes. You will learn a lot here if you can carefully pick through any advice offered, but if you're not confident to do that yourself at this stage, we'll do it for you

!
So...
1. regular vet visit not needed.
2. pillowcase is perfect for transport, turned inside out as Wokka suggests, and tied as Bluetongue1 recommends (strong rubber band is good). Place the pillowcase, with lizard, in a box so that no one sits on it or otherwise accidentally crushes the animal.
3. try and find an experienced fellow reptile keeper nearby to answer questions you may have as your keeping career moves forward. If not, refer here...
Jamie