AdBlock should not negatively impact browser speed. There will be a bit of a delay when you first open your browser while it fetches your AdBlock filter lists. After that, pages generally load much faster because you're not downloading ads.
If you're noticing a serious lag when you start up your browser, there are a couple of things you can do. First, don't subscribe to more filter lists than you need (doing so can slow down your browser). Second, avoid having a large number of tabs opening automatically every time you launch your browser. If you do, then after AdBlock downloads all those filter rules, it immediately begins applying them to your open tabs to block any ads they may contain.
AdBlock definitely will not affect the overall performance of your computer. It's a browser extension (a little piece of JavaScript code that extends the features of the browser it's installed in). It can't affect anything outside of the browser.