Websites don’t have PR!
PageRank is assigned to individual pages, not websites. The PR of the homepage is inconsequential if you do not have a link from the homepage. It is the PR of the page where your backlink is placed that matters.
Keep in mind that you are not able to see the true current PR for any webpage, only what it was at some point in the past, rounded to the nearest whole decimal. The real PR is updated continuously and not available publicly. Every page that is indexed and not penalized will have some PR. Even a new page is assigned a fraction of PR (0.15) as soon as it is indexed.
Also, keep in mind that every new webpage starts out with a small amount of PR that grows as new backlinks are indexed. Look for pages that are likely to receive high amounts of traffic, as those are the type of pages that will tend to grow in PR. Your PR1 backlink could become a PR 4 backlink in a couple of months and perhaps even higher over time.
As to your website being “General” that isn’t necessarily a problem. Search engines do not consider the topic of a website when ranking in the SERP. They only look at the topic of the individual page. Each page of your “general” website can, and should, have a very specific topic. You can focus on getting each individual page to rank for its’ particular topic.