The AWS Elemental MediaConvert service transcodes files on-demand. The service supports output templates which can specify output parameters including resolution, so guaranteeing a 720P maximum resolution is simple.
AWS S3 supports File Events to trigger other AWS actions, such as running a Lambda Function when a new file arrives in a bucket. The Lambda function can load & customize a job template, then submit a transcoding job to MediaConvert to transcode the newly arrived file. See ( https://docs.aws.amazon.com/lambda/latest/dg/with-s3-example.html) for details.
Limiting the size of an output file is not currently a feature within MediaConvert, but you could leverage other AWS tools to do this. Checking the size of a transcoded output could be done with another Lambda Function when the output file arrives in a certain bucket. This second Lambda Fn could then decide to re-transcode the input file with more aggressive job settings (higher compression, different codec, time clipping, etc) in order to produce a smaller output file.
Since file size is a factor for you, I recommend using QVBR or VBR Bit compression with a max bitrate cap to allow you to better predict the worst case file size at a given quality, duration & bitrate. You can allocate your '200MB' per file budget in different ways. For example, you could make 800 seconds (~13min) of 2mbps video, or 1600 seconds (~26min) of 1mbps video, et cetera. You may want to consider several quality tiers, or have your job assembly Lambda Fn do the math for you based on input file duration, which could be determined using mediainfo, ffprobe or other utilities.
FYI there are three ways customers can obtain help with AWS solution design and implementation:
[a] AWS Paid Professional Services - There is a large global AWS ProServices team able to help via paid service engagements.
The fastest way to start this dialog is by submitting the AWS Sales team 'contact me' form found here, and specifying 'Sales Support' : https://aws.amazon.com/contact-us/
[b] AWS Certified Consulting Partners -- AWS certified partners with expertise in many verticals. See search tool & listings here: https://iq.aws.amazon.com/services
[c] AWS Solutions Architects -- these services focused on Enterprise-level AWS accounts. The Sales contact form in item [a] is the best way to engage them. Purchasing AWS Enterprise Support will entitle the customer to a dedicated TAM /SA combination.