[rally]

Hypothetically speaking
Most of the comments above are probably aimed at the 7-10yo
A 12 year old will already have a critical eye for quality.
They will be expert users of the internet and will probably already have done their research.
They will start asking for stuff higher up - Planewave 12.5" on Ascension Mount, or Astrophysics 4" on Paramount !

They will probably already know that there is almost no colour to be seen through an eyepiece and probably want to go down the astrophotography route - but of course they are only 12 yo so they have no idea how deep they would be getting or difficult and hard it is !

So to spend less than the price of a Precise Parts adapter on them, or about the cost of a single cheap but useable quality eyepiece going to seem like an insult to their interest.
The telescope is going to end up an all of family piece of equipment - find the extra dollars and buy something half decent.

Truthfully I wouldnt even bother spending $150 on my son if he showed genuine interest in astronomy at the age of 12yo
If I spent that little it would be counterproductive - but then I have never understood the rationale behind Kids meals at hotels and restaurants where you feed them low grade cheap meals comprised of chips, reconstituted nuggets and carbohydrates instead of good food
Why would we feed the next generation rubbish food !

Why would we buy them equipment that is more likely to quell their interest due to its limitations and low quality than buy them better quality equipment.
You say on a limited budget - but surely this is a case more of limited priority than true limited budget.
Just wait alittle longer, buy components for Birthdays and Christmas.

Sure you dont want to waste money on a passing fad, but at the same time there are star parties etc to evaluate their real interest, so once established - get the family a decent system that they can grow into.

Mine may not be the most popular opinion, but I dont see any value (especially on a limited budget) of buying gear that will need an immediate upgrade (ie doubling or quadrupling the initial expenditure for eyepieces or mount of OTA) just to maintain interest and save wasting time on failed viewing sessions and tweaking to try and get a half decent view in the first place !