Design trends in recent years have paid a lot of attention to this. In the past, what was in the other room didn't matter. it's OK now! If you use chrome in your bathroom, you might consider a two-tone finish on your Inside Door Handles. You'll see a touch of chrome combining your bathroom furniture with door handles for a powerful yet subtle statement. Alternatively, your cabinets may have a Hamptons feel, which means you can opt for Hamptons-style levers.
All materials are not created equal. Consider your environment, whether you are close to the coast or in a particularly windy or humid environment. There are a variety of materials, but in this case, a micronized finish or brass product is the best. You can learn more about micronized finishes here. Also, consider the use - if it's going to be subject to heavy use and heavy traffic, the stronger the material, the better. A good guide is to check the warranty. A good warranty should be at least 10 years, and a mechanical warranty should be 10 years.
Whether you choose a round handle or a lever handle, it almost certainly comes down to two things. The look you want, and who will use it. Round handles are mostly used for old houses that fit that look. However, lever handles are also available for those period-type homes, so it's up to you. Remember that lever handles are easier to use, while round handles are often difficult to turn.