Start writing as early as possible (the summer before application season if possible) and have many eyes read your statements, regardless of if they are in science or not. My rule of thumb is that even a non-science person should be able to get the gist of my writing, and that is how I know I have clearly conveyed my point.

Write concisely!! Admissions officers are reading hundreds of applications, so to help yours stick out, do not belabor the point. Get to the point quickly and clearly.

ChatGPT is an excellent tool (for editing and clarity), but it can't replace you. I recommend the following workflow - write out your draft to the best of your ability, use ChatGPT to tighten it up, then show it to a peer/advisor before doing final revisions.

Make your application as specific to Penn (and/or Philadelphia) as possible to show that you've done your research on why Penn/Philadelphia is a good fit for you. To do this, do your research on what Penn resources are available or what about the Philadelphia culture would help you succeed as a grad student.

Some of the best advice I got when writing personal statements is to write them like a story to engage the admissions officers. There should be some sort of theme throughout your story that explains how you got to this point and your inspiration for pursuing a PhD, as opposed to going into industry or a masters degree.

In your research statement, do not overcomplicate the description of your project to try and sound "smart and fancy." Chances are that your application reader is not an expert in that field of research, so you want to ensure a general scientist is able to understand WHY (hypothesis/rationale) you did your project, HOW (briefly) you did carried out experiments, and WHAT you found. Two of my undergraduate PIs served on their respective admissions boards, and some of the best advice I got from them is that research statements are meant to demonstrate you are able to think like a scientist - it is not necessarily about how complex and successful your research opportunities were, but instead your understanding and passion for your projects.

Make sure there are multiple PIs at each institution you are applying for whose labs you are interested in potentially joining. Feel free to name these PIs in your personal or research statement as reasons you are interested in the institution. It is also beneficial to discuss specific facilities or programs at each institution that excite you and make them stand out compared to other institutions you are looking at.