Jinteki Net Damage

I'm assuming this is only Core Set and Honor and Profit, no?

You should use some of your influence! There's a lot of weakness of Jinteki in the core set, so you should try to cover them.

I suggest buffing your economy with something Adonis Campaign, PAD Campaign(drip econ but a bit costly to trash), Mental Health Clinic.

Also, early game, you actually want to keep the runner out, especially R&D since if ever they access Junebug or ShiKyu, they can easily trash it. So some cheap early game ice might be a good place to spend some influence. Ice Wall or something. Lots of neutral cards for that as well; Guard, Wall of Static, Enigma, etc. Maybe drop the some of the Data Mine(0 trash cost, it's vulnerable in R&D) and Neural Katana(only 1 sub, kinda easy for the runner to break).

Try to play some Neural EMP, since it's a good finisher once the Runner is vulnerable. You could also try to lean on some tag punishment. Maybe you want to consider 1 copy of Scorched Earth since it makes Snare really dangerous for the Runner. Maybe even 1 Closed Account if you find yourself playing against a Runner with a robust economy.

As for agendas, I suggest dropping some of your Priority Req. It's a good card, but since you're not running a lot of End the run ice, it'll be hard to score. Medical Breakthrough might not be a bad idea, then you can lean on some minor fast advance option if you find it's too difficult to flat line the runner. Sansan City Grid would be good choice for this.

Hope that helps dude.