The pros and cons of each are all over the internet. Price and flexibility, which of the two routes looks better when applying for an airline regional or legacy, does it matter? More importantly which better prepares you?
Either one is fine, though I'd make sure you seek a good instructor for a part 61 and follow a part 141 syllabus (available through ASA, Jeppesen, King Schools, etc.) when you do yours to verify you covered all the bases.
At that stage of your training, future employers really won't care that much whether you did your training as a 61 or 141 student. They are going to be much more concerned with your professional flying record and later certification and checkrides.