If you are not looking to attend a top tier law school, it doesn’t really matter what undergraduate degree you get and who issues it as long as the institution is accredited. Your LSAT and possibly an interview will make the entrance decision.
Currently, there are loads of empty seats at American non-top tier law schools. Being an attorney is not what it used to be in terms of income, advancement, etc. It has changed drastically in the past 30 years.
I have hired associates who have BTLs, pre-law degrees (whatever that really means) and a BS in IT. I am more interested in where they attended law school, where they interned, what courses they took in law school (and grades earned) AND that they have passed the state Bar Exam. Except for my children and spouses, I do not hire anyone who has not passed the Bar Exam and is licensed.
If you expect to earn a paycheck while studying for the Bar Exam and learning on the job, best bet is to start with a government agency (DA, etc) who uses tax dollars to underwrite your cost,