IP law is now developing into a major sector of law because of the widespread use of the internet. In fact, developing countries are developing wireless networks for their citizens.
I'd say that an engineering degree is a very practical stand alone degree and if you decide to go to law school, your engineering degree will create a good "combination degree" with your JD. Law students with combo degrees such as engineer/attorney, doctor/attorney, CPA/attorney, pharmacist/attorney usually tend to do better in law school than non-combo degree students and most importantly, they tend to receive better job offers.
I would get a practical undergraduate degree and combo it with the law. In law school you can take some IP classes, but you will ultimately take classes with help you focus on passing the bar exam.
Once you are done with your JD, you will probably want to go back and get an LL.M in IP. An engineer/attorney with an LL.M in IP will be a serious asset to any firm.
If you have an opportunity to clerk at the USPTO or at a firm, then jump at it.
Most law students fight over clerking jobs, so take what you can get!
The IP attorney that I send work to went to DePaul Law school and he is a big fan of DePaul. Check it out.
Good Luck!