If you do want to do at least some of the patent work yourself, then start with a provisional patent application. This is an affordable way to get the process started without overstepping. Later, you can have your patent attorney help you to finish the process or use a patent agency to do the work for you.
Instead of trying to go it alone, handle the provisional patent application yourself. Then, have an attorney handle the claims and the filing of the permanent patent. Doing this will reduce your costs as much as possible, or at least defer them long term. Ultimately, this will be the best way to save money and still get a patent that holds up as explained in https://www.techtimes.com/articles/249715/20200518/how-inventhelp-gets-new-inventors-onto-the-right-path.htm post.
You may think that anyone can take the patent and put it in place, but that is not the case. Rather, you have one full year to put your patent application in place or no one can do so. Once that invention has been in the market place for one full year form the initial selling point, not even the original inventor of the invention can apply for a patent for it.
Instead of allowing this to happen to your invention, work with your patent attorney to get your patent in place as soon as you can. You may also want to consider the benefit of a provisional patent application since this is not a published application but does not start the one year rule on its own. You get the benefit of the early filing date with a provisional patent as you can see from this https://www.valuewalk.com/2020/05/medical-invention-covid-19/ article.
Do not avoid having the patent put in place since it can take time for the process to get started. Do not wait until the last minute to get your patent application in, either. There are very strict requirements in place that could limit your ability to get credit.