How viable would it be to reroll a character and try to only fly precursor ships? Obviously it would be expensive in ISK to skill up and buy equipment. Do the ships offer enough to be able to do PVE to get established? (there may be a little sleep deprivation behind this question…)
You have a bit of a chicken and egg problem unless you want to buy PLEX from CCP and inject a lot of skills - and character skills without the matching player knowledge and experience is a recipe for disaster (i.e. very expensive kill mails)
I recommend that you stick with one of the traditional empire ship lines - all are viable for PVE - until you can afford to fly precursor hulls without concern for the cost. You’ll also find that pirate hulls, particularly the Guristas, excel at PVE once they fit comfortable in your budget.