I can't afford weekly lessons, and wouldn't have enough practice time to make them worthwhile anyway. So what would you say if a prospective student asked you about monthly lessons?
The key thing I picked up on was you mentioning practice time. If you do not have much time then weekly lessons are pretty useless, you will not use your teacher enough. You may end up having them drag you through bar by bar until a piece is finished, not worth your money. If you have monthly lessons you must approach your studies in a slightly different manner.
With weekly lessons the teacher is constantly adjusting your efforts, with larger time gaps you must do things on your own for greater periods of time. You really do need to experiment a lot on your own and learn as much of the pieces you can on your own. Then use the teacher to improve upon what you managed to do. The problem with long time between lessons is that you often can go off in the wrong direction or do things less effectively. If you are ok with plodding along by yourself and willing to learn from mistakes that you might have harvested for a number of weeks, monthly lessons are fine. It actually doesn't matter if you do something completely wrong but think it is right, when you are shown a better way it will make a lot more sense because you can relate it to how you where doing it less effectively. I would advise taking at least a 2 hour lesson with the teacher every month so you can go through everything you have done in detail. One hour per month is quite limited but might be ok if you get through all the work you did in the month. Half an hour is pretty useless unless you are just using the duty of reporting to a teacher as a motivator.
Keep a journal of solved and unsolved problems you might come across while you work alone during the month. Keep a detailed inventory of challenges you face so when you meet with your teacher every month you can get through the most important issues without the teacher having to assess everything themselves. You should take control and know what you need more help on and ensure that you have it all mapped out and planned neatly. If you find it difficult to pinpoint your own problems and working alone then monthly lessons probably will not be for you.
Having a teacher is a good motivator, you have someone to answer to and not just yourself. No matter how you approach it really, it is a good idea to have a teacher, go for it.