I don't have any advice on hardware choice, but there have been a lot of negative comments and I felt compelled to lend my support - from personal experience.

I remember my (10 years younger) brother playing Sticky Bear Alphabet on an Apple2e before the age of two. Hitting a letter on the keyboard cycled between two words for each letter - each with a simple animation. Within a short time he progressed from random bashing to being able to keep the state of each letter in memory - so that at ANY time you could walk up to him and ask him "what is the next picture for letter X" for every letter, and he would know. This was while he was still on the bottle and still in his first baby seat.

I attribute his early exposure to this educational game to have significantly advanced his language skills. One distinct memory I have is just before he started primary school - I knew he was reading very well but he being cocky about it - so thinking I would cut him down to size I asked him to read the legalese of the back of my driver's license - which he promptly did reading "The commissioner of police hearby grants the bearer..." - which took me quite by surprise. It was obvious he hadn't seen the larger words before but had fairly fluently just sounded them out as he went - and I thought to myself "oh my god, this year they are going to teach him how to spell CAT and DOG".

That is the downside. School bored him. In class he would zip through his worksheets and then assist his classmates - and get in trouble for talking/helping - which really discouraged him. A good teacher would have extended him, but generally the public school system is not set up to handle an anomally like that.

I directly attibute his early intelligence and confidence to the alphabet game he played as a toddler. He has always been very social and now at 25 is a teacher. Too much computer time could create other issues, but overall its been a positive benefit. You will need to pay attention to counter-balancing this with physical and social activities. I will be looking to do the same in a while with my (now 1 year old) baby girl.

Last year I did a course "Electronic Measurement" at USQ which dealt a lot with EMC compatability, PCB layout, noise resistance, etc - a lot of really non-obvious stuff until you read it.

From this I've ended up with bundle of very enlightning PDFs, some of which I'll list below. I'm not sure if these are what you are looking for, but they certainly match your price range. I recommend anyone every using an op-amp read at least the first one, which I found quite amazing - for illustrating the different return paths AC and DC take across a PCB. In general, search the application notes of the device maufacturers - particular Analog Devices.

+ AN-345 Grounding for Low-and-High-Frequency Circuits.pdf
+ EMI and Layout Fundamentals for Switched-Mode Circuits R.W. Erickson.pdf
+ AN202 An IC Amplifier Userâ(TM)s Guide to Decoupling, Grounding, and Making Things Go Right for a Change.pdf
+ A Designer's Guide to Instrumentation Amplifiers 3rd Edition (Kitchin & Counts, Analog Devices 2006).pdf
+ Reducing RFI Rectification Errors in In-Amp Circuits (Analog Devices AN-671).pdf
+ Op Amps For Everyone - Design Reference (Ron Mancini, Texas Instruments 2002).pdf
+ Analog Dialogue vol39n3.pdf
+ The Instrumentation Amplifier Handbook (Neil Albaugh, Burr Brown Corporation).pdf
+ Shielding and Guarding (Alan Rich, The Best of Analog Dialogue 1983).pdf
+ Errors and Error Budget Analysis in Instrumentation Amplifier Applications (Analog Devices AN-539).pdf
+ PCB Design Tutorial RevA (David L. Jones, 2004).pdf

If you can't find them yourself, I could upload them (if someone could provide a simple service to deposit them at.)

If you decide it appropriate for your neice to read, it may spark some discussion comparing school maths/science to university maths/science. Find out what she is interested in.

One way ahead is to encourage her to consider only a five year career plan. Neither she nor yourself should feel her choices NOW lock her into a lifetime in one career. People often don't find out what the REALLY want to do with their lives until they've been in the real world for a few years. She should leave her options open. Encourage her to do whatever she feels like doing now, but whatever course, keep some higher level maths as a minor. It may end up giving her the edge someday.