Many people have employees working at home (for example - where I work). It can work great, you can use a clock in/out system on their computer so you and them know exactly how much work they are doing. Obviously you need to find someone you feel you can trust, but that is the same if you are hiring someone to work in an office.
If they are working from home, you can actually benefit from broader availability throughout the day, as opposed to when someone is only working when in office...
For your specific case, it makes sense to hire someone to work at home as you are not set up with an office with other workers, and it can be also uncomfortable, yichud issues etc.
You can pay per month based on x amount of hours and the worker will make sure to do those hours.
As an aside, for your first hire, and all, you must have a contract, with all details specified so know misunderstandings later. For example, do they need to clock out for a snack, Mincha etc. Many templates can be found online.