What's a realistic landing page conversion rate for PPC traffic?

There's no universal benchmark
You'll find claims that "average conversion rate is 2%" or "e-commerce lands at 3%." These are mostly meaningless. Your conversion rate depends entirely on your industry, offer, audience intent, and page quality. Don't compare yourself to an invented average.
What actually determines your rate
High-intent, low-friction offers (signing up for a webinar, downloading a guide) commonly convert at 10-40%. Low-intent offers (a free trial requiring credit card) or commoditized purchases (generic e-commerce) often convert below 3%. Subscription software trials typically fall between 5-15%.
Your baseline is your industry
Instead of chasing an industry average, track your own baseline: what does your current page convert at? Then test incrementally. If your page converts at 2%, improving it to 2.5% is solid progress worth celebrating.
More important than the rate
Focus on cost per acquisition (CPA) instead of conversion rate percentage. A 1% conversion rate from cheap traffic might produce a lower CPA than a 5% conversion rate from expensive traffic. A 2% conversion rate on a page that loses money isn't useful.
The path forward
Establish your current conversion rate, then test to improve it by 10-20% increments, which is realistic and meaningful.