The problem when it is suggested to go with a Buick 350 is while it is a direct swap you first have to find one that is still in good running condition and since they have not been in production in nearly 30 years and depending where you live finding one might not even be possible and if you find one that is not running and you want to use it you are at the mercy of some machine shop that you have never dealt with before to go through it.With machine shops being few and far between now, overhauling an engine would not be cost effective. My budget is limited, .
So the reality is since money is an object for you I would just work with the 3.8 you already have but if you decide to spend the money and want affordable power that is where a SBC makes sense, it is available new from GM with a factory warranty or rebuilt by many aftermarket vendors with a warranty and parts are inexpensive and available everywhere.
While I have nothing against a Buick 350 swap it typically is not a budget minded swap by any means.