If you want to gain reputation, it is best to apply for it yourself, so that the patentee is your own.
It is worth mentioning that the granting of patent rights may take a long time, because first it needs to be disclosed, and secondly it needs a substantive examination process. If you respond to examination opinions many times, it will take at least several days for your patent to be authorized. years, and it is still in compliance with various provisions of the Patent Law and Implementing Rules.
Of course, you can get the application number and application date when you apply to the Patent Office. This protects your rights, but it has no practical significance until the patent is authorized. In addition, if it is just for "reputation", you still need to wait for the patent to be published and searchable by the public.
In addition, if you go through an agent, since it includes the application and substantive examination as well as the annual fee after authorization, especially if you need an agent to write it, it will not be cheap in total. And whether you use school funds or pay for it yourself, you need to have a certain understanding of the legal significance of the claims. Otherwise, poorly written claims will either fail to pass the substantive review, or if they can pass, the scope of protection will be very, very narrow. Things that are ugly will look bad to people who understand them. This may not be in line with your original intention. . .
In view of this, the channel through which you apply depends on your purpose. Because you say that you do not need to consider making money, it may be an invention that is less commercial and prefers research or academics. Assuming that your goal is to finally obtain authorization, you can do a search first to see if there are many similar existing technologies. If you are very confident in the creativity of your invention, or it is indeed a very good technology, I personally think it is still worth applying for it yourself, but you must have an understanding of the basic structure and legal significance of the patent, and the disclosure letter must be well written. Throw everything to the agent, regardless of skill level. The agent takes too many cases and doesn't pay much attention to personal entrustments. You still have to control the quality of patent drafting yourself.
A little insight. . .