When a company takes shares out of circulation, it drives price up in theory because there is less supply and demand has not changed, but that does not always take place in a free market. Shares outstanding also may increase if the company sells more shares to the market giving them more cash to spend as they wish.
If you see shares outstanding increasing, you may want to take a step back and see if there is a reason why it is increasing. It could be all apart of their plan which is fine, but if the company is struggling for cash and keeps selling shares to the market, that could be an indication of greater issues.
The ideal situation would be the company slowly purchases their shares back, increasing the value of the stock and the company becomes dependent upon their own cash flow. Of course each company has their own plan for outstanding shares and you need to fully understand what the company has in mind. Ideally you want to see the company sticking to their game plan and going with the flow. This should not be a huge issue, but it certainly can if the balance of shares begins to swing wildly.
Take a look on the Internet and see how others use shares outstanding in their research of a company. This could also lead into liquidity because smaller companies are not as traded and they may not have as many shares outstanding. All of these can be affected so be sure to take a quick glance and see what is going on. If you get stuck, reach out to an investing community or investing professional as they can help to point you in the right direction. Share count is an interesting factor to take a look at and it may swing your research into a direction you otherwise would have skipped.