The shoe that was worn most by Civil War soldiers is generally accepted to be what is now known as the latchet shoe. As far as we can tell they were issued in their thousands, ideally three or four times a year, possibly in one of four sizes, which is a clue to the reason they had open sides. A closed sided shoe might seem more practical as it keeps the weather out, but the open sided style is better able to fit a variety of foot shapes as it has a built in adjustment.
What you need to look for first in a good quality latchet shoe is sturdy all leather construction. A hand made shoe has butt stitched side seams, whereas a machine made example will generally have overlapping seams. There are no inherent problems with non hand stitched shoes, but there are some pitfalls to avoid. Try to find a pair that has a reasonable thickness of leather and pay attention to the side seam positioning as this is an easy mistake to make in construction and results in a poorly fitting and ill-shaped shoe.
This is a picture of an actual 17th century open sided shoe from a book called The Romance of the Shoe as far as I can work out and is ideally what you should be looking for. Although this is not a cheap option, a well made pair of latchets should last you a long time if they’re looked after. The square toe isn’t necessary, in fact most shoes of the period had round toes and the theory is that they were more sturdy and harder wearing than square toed examples. The side seam is level with the fastening and also notice the shaping around the heel.
And here is a photo of my latchets that I use for reenactment. They were made by Sarah Juniper to replace a pair of hers that I had worn for twenty years. This is the ideal to aim for in a soldier’s shoe. They are also fine in a pike push. I can vouch for that personally.
In this detail from a french engraving, cropped to show the legs of a pikeman, you can see the construction, the back seam, the closing method all in the one image. Although the French soldier has ribbons to fasten his shoes, they are in every other respect what would have been worn on the field of battle in the 1640s. Etching by Abraham Bosse, Paris 1632