I usually work with stacks of confocal images and multiple IF labelling with Imaris and Image Pro software. Imaris is easier, has two ready procedures of image thresholding: absolute intensity or local contrast, but if you need a software with wide range of possibilities of image adaptation prior to analysis Image Pro will be better. Third option, always worth of trying before use of expensive commercial software is free Fiji (previously ImageJ), it has also plenty of possibilities.
I also recommend you to use Fiji/ImageJ, which can read jpeg formats. However, jpeg format is not a good one because it removes information. ImageJ can read about 180 bioformats, including files from common microscopy softwares (AIM/ZEN, NIS, etc).
If you want to analyse big data (from LightSheet microscopy for example), you can download a free Fiji plugin called MaMut (https://imagej.net/MaMuT). If you need to process many images in the same way, you can also use the free software ilastik (https://www.ilastik.org/download.html).
Which type of microscope and software do you use? Most imaging software also has build in analysis tools and a light version of these tools is usually available for free to download on your pc. The biggest advantage with this software is, that it is specialized for the type of files generated. That said, ImageJ/Fiji can open and convert all file types as well.
As Latitia recommended, don't go for jpeg files, there you have already lost a lot of information from the original picture.
I also recommend to watch a tutorial online, most microscope companies have very nice videos about image acquisition and analysis.
ImageJ and Fiji are free, and there are user forums. But it can be clunky. I find Celleste more powerful and easier. You can get a 14-day trial to test it out or have a rep come to show it to you. Let me know if interested and I can help with the arrangement.
Info and how-to videos: https://www.thermofisher.com/us/en/home/life-science/cell-analysis/cellular-imaging/cell-imaging-systems/celeste-image-analysis-software.html
I highly recommend you to use as raw format of images (what you directly get from your computer connected with microscope) before you fed into any image analysis/processing software. Next, depending on what information you want to extract from the Image, you choose the software. Most people already have recommended you to use either imageJ or fiji. These are very user friendly and covers all the need, whether to calculate image intensity, or S/N, or further processing of your image data.
Jason A Kilgore recommended Celleste but please note Celleste is a derivative of Image-Pro and Autoquant from Media Cybernetics. AutoQuant in particular has some long standing concerns regarding the algorithms, please see this related question https://www.researchgate.net/post/Have_you_ever_output_the_PSF_from_Blind_Deconvolution_and_shown_it_converges_to_the_true_PSF_of_the_system_If_so_can_you_point_me_to_the_data