Hi there Arnie!
At the risk of being over tekkypikky! Can I make a couple of points?
Your post is entitled "DI Box thingy" but you go on to talk about re-amping? Not quite the same assembly of electronical bits mate.
Second blooper..." boost the signal from line to instrument"(? Guess you mean amp?) No, one of the important parts of a re- amp box is the ability to ATTENUATE the signal to approximate the level* an amp would get from a guitar.
"Open budget"? The top bollox is the Radials. Nice but £200+ .
Don't know if these ship to EU..
Welcome to Orchid Electronics Very well respected, top value kit their "Amplifier Interface" as they call their re-amper is just £56. I could not make one for that and get very pissed on the profit.
*But, despite what you might read/be told, the guitar amp does not give a flying fffffig! what the source impedance is!
Dave.