Concrete core drilling isn't something that you generally have the need to perform on your own, as it is a complicated procedure that rarely needs to be done in domestic environments. However, if you're about to build a furnace, or if you need to put the weight of a house further down into the ground, you need to use a core drill. If you aren't a professional core driller, it might be hard to know what equipment you need. When thinking about what type of drill you should get, there are a few things you need to consider.
Handheld units are generally too small to perform any significant core drilling jobs. They might seem attractive as they tend to be cheaper to rent than larger machines, but you need to evaluate if a handheld unit is enough for the project you are working on. If your primary objective with the drilling is to test concrete core strength, then a handheld unit most likely won't be enough as you won't get a large enough sample. If your main purpose is to drill holes in concrete pipes for plumping or reinstallation, a handheld unit is preferable, but for any other core drilling work, you're better off with a standalone unit.
If you're working close to your house, the easiest power source to use is electricity. As these types of drills are the least complicated energy wise, they are also cheaper to rent. If you're working in a more remote location where you don't have access to electricity, you should opt for a pneumatic model, or a unit that uses a hydraulic system as a power source. Just remember that hydraulic units will need some sort of fuel to run, and that will add to the cost of you renting a concrete core drill.
If you're drilling on a flat surface where the drill will be able to stand, you should get a unit that has a vacuum feature. This means it will apply suction to the surface to make itself stand steadier. If you're drilling on a wall or an uneven surface, however, you don't need this feature as it might be dangerous to use in those conditions. Instead, you should opt for spending a little extra money on anchors especially made for core drills to make sure it's able to stand safely. As an extra precaution, this is also something you could do even if you are using the suction feature on a flat surface, as it will only make the drill steadier.