IFF the legal system of the country seeking extradition is trust-worthy and offers the same guarantees of human rights as the UK one, why would the charges need to be credible at all? The accused could be sent to that country, with the expectation that the trial would quickly go in the accused's favor.

Of course, they do have to be charges for something which would be illegal in some way in the UK as well. If the US criminalized ice cream consumption, you would not be able to extradite someone in the UK for having consumed ice cream in the USA, of course. But this is not the same as, say, extraditing someone accused of murder in the USA who is not known to have been physically there - the extradition judge may be ok in not looking at the evidence that the charges are based on (except maybe to ascertain whether they may be a sign of a politically-motivated trial).

I wonder about this. Let's say that in the US I'd have a budget of about $3000 to spend on the trial, without having to completely ruin my savings.

Would that be enough for housing, airline tickets (back to europe), and the trial/lawyers/bail/court fees in the US?

If frivolous extradition/trial would ruin me financially, I'd rather extradition procedure took the credibility/frivolousness of charges into account...