A decent quality paint that we use on the bulk of our flips and renovations is Olympic One interior flat available at Lowes. You can color match and tint to just about anything and it has very good coverage, plus touches up well. Kilz is a great oil-based primer for sealing new wood and covering up smoke damage or smokers long term inside. For spot work and new wood, we prefer Zinser Coverstain. It's a little more money but has better coverage. Most times Kilz will require 2-coats on new wood.
If you are not an experienced painter, buying or using a sprayer is waste of time and money. Best thing you can do is an old fashioned brush & roller...don't ever buy cheap brushes except for oil based priming. For finish coats, always use Purdy or comparable Wooster brushes. Clean them well and you'll have them for years. When painting, keep a few grocery type plastic bags on hand. As soon as you put a roller or brush down, wrap it up. If you are quitting for a few hours or overnight, double the bag and wrap it up & lay flat. My crews and I do this and use the same brush and roller for a week without cleaning. Lowes has some new "pre-wet" rollers that we used this week with good results.
@Michaela G. - welcome to landlording. What color is the rest of the house? You will probably be best to sand as much of it off as possible. Depending on the color of the rest of the house, you might want to use a Zinser 1-2-3 latex primer tinted to match the color of the house. It will take several coats but you can mix small batches at a time in a $4 painters cup. For you other brick paint work, see if you can find an adhesion primer. Sherwin Williams used to have the best product but I don't think they make it anymore. They do have a special paint for stucco which will work well on brick. Most of our exteriors are done with SW Duration or Emerald products. Even our flip houses. It costs us more but the results are great long term.