Vince -
You've asked an excellent question and added some attachments that help demonstrate your issues. Composition and Light are issues, but from a technical standpoint, let me add the following:
1. Your XSi will produce wonderful pictures, but this is an older model and has a number of limitations of an entry-level DSLR from 2008. These "limitations" are that many automatic capabilities and / or settings found in newer cameras do not exist on this model.
2. You cannot set limits on the AUTO ISO range on this camera - an example limitation of the XSi / EOS 450D. In the context of your shutter vs aperture priority question, I suggest too that you manually select your ISO rather than letting the camera run on auto. Use 100 / 200 / 400 just as you would select film speed for a given situation. ISO-800 is grainy on this model, but still very usable. ISO-1600 really isn't going to be acceptable.
3. Regarding background on the camera, be sure you've downloaded a copy of the PDF manual. Old Canon manuals can be found here:
http://www.usa.canon.com/internet/portal/us/home/support/camera-user-manual Several of the points listed below will require that you consult the manual to find the menu section within the camera to review and / or update the setting.
4. Looking at the first picture from a technical aspect, the low(er) light is the issue. This image would look better if shot at f/8. But, already you're at 1/40 shutter @ 80mm @ ISO-400. The smaller aperture will look better for your lens performance as well as giving sharper results across the frame and through a greater depth of field. Given this camera and lens combo, you'll need a tripod in this shooting light.
5. Another idea assuming you're shooting JPEGs from this camera, use the "Landscape" picture style when shooting a landscape such as the first example. Use the White Balance settings as well. Auto (AWB) might be best for this image in the mixed shade and daylight. The daylight setting might work as well.
6. Again assuming JPEGs, assure that you're shooting in the highest quality producing the largest files capturing the most detail the camera's sensor can capture.
7. Use the largest cards the camera can support. If I remember correctly, Canon Rebel's circa 2008 couldn't use a CF card larger than 8GB. The high quality image setting will eat up these smaller cards relatively fast, even more so if shooting in RAW. I have some old 4GB and 8GB cards from a long ago sold XTi where the cards are just gathering dust. If you need some, just send me a note and I'll send them to you.
Back to your questions about pictures that look like others here and across the internet. Those images, I can promise you, are heavily edited aka post processed. At the minimal you can visit the Canon website and download the Digital Photo Professional 3.15, the software that works with you camera's RAW files and JPEGs. The software is free. There's other free software across the internet for basic and mildly advanced editing such as working on the saturation, noise reduction and contrast. The USA Canon website has only an "updater" file that assumes you have the original software from the CD that came with the Camera. If you don't have the CD, you can get an copy of the software from the disk from Canada and other Canon website locations. You'll be looking for "EOS Digital Solution Disk Software 29.1A for Windows" or similar for Macintosh.
Another difference in other images is they're using higher quality lenses. Your 75-300 is a very basic zoom lens. Your light, shutter priority and ISO decisions are forcing the aperture wide open. Changing to Aperture priority or Manual and using this lens in situations where f/8 to f/11 can be used will produce better results from this lens model. As mentioned by others, where handholding without a tripod, shoot in situations and use camera settings with a shutterspeed of 1/200 to 1/500 (or faster) depending on the focal length set for your zoom lens.