Cost aside there are a couple of things to consider when choosing a safety razor. The first being the handle of the razor. You want a a razor that isn’t heavier on one end rather a well balanced tool. It should be comfortable and allow you to maneuver the razor across your face with ease. For the most part you also should look for a razor that isn’t too light (some exceptions to this rule) or too heavy. A razor that is to light may cause you to add more pressure when you shave, possibly cutting yourself. A razor that is too heavy could result in a similar predicament because of too much natural pressure from the weight itself.
The second thing to consider is the razor head. More specifically the razor gap. The gap between the blade and the safety bar should be the same on both sides, ensuring the same experience regardless of what side of the razor you are using. Some razors will have a larger gap than other but what you are looking for is a consistent spacing. You will run into this issue most often with lower quality razors, not so much with more reputable brands like Edwin Jagger or Merkur along with several others.
One issue is that razors tend to be purchased online for the most part, so you are forced to rely on reviews of the razor in order to make you decision. Unless of course you are fortunate enough to have a shop nearby with a selection.
For more information on choosing your first razor check out this article with suggestions on your first razor.