Client Solutions in PE- Career Dilemma

Hello everyone, 

I am a sophomore at a complete non-target who wrapped up recruiting for this semester. I did not have much luck breaking into IB but by some stroke of luck, was able to land a Client Solutions internship at a big PE firm. Now I am very grateful for the opportunity and accepted the offer, seems like it has great WLB and good pay. However, now very very early stage opportunities are arising from a decent GE shop (big name in GE but nowhere near the name of the PE firm overall) and I'm here seeking guidance on what my plan of attack could be, as I don't wish to jeopardize my other offer and wanted to see career progression of both. Now I know its not like i have the GE offer already but I don't see myself in Client Solutions for long but was wondering if I could pivot into IB/GE later on for FT recruiting using brand name and other relevant finance internships in GE as leverage (as opposed to being a nontarget trying to break in) Also, the GE shop doesn't have a great track for returns and historically, its exit opps have not been great from analyst program while being in a location which is unideal. Long term, I see myself in hopefully a great top-tier VC and also grad school so was wondering whether Client Solutions --> IB ft recruiting next year/MBA  would be the way to go or still keep on trying to recruit?  I think Client Solutions is awesome but being on here and reading the forum, it seems like there might be limited upward mobility and if I am particularly interested.