I get asked once in a while for beginner tips, so here's my advice...
- 90% of the reason to trade up to an SLR (that you can afford) is eliminating shutter lag. If you have kids, it will save you from an aneurysm.
- A kit lens is all you need, but consider buying a prime lens like the 50mm f/1.8. It's cheap and great for low-light and nice bokeh.
- Feel free to go auto-everything for a little while, the embrace Aperture Priority (with +/- compensation).
- Fill the frame with your main subject, but don't "bullseye" a person's face.
- When in doubt... use the rule of thirds for composition.
- If you can afford it, get Lightroom. It fixes lots of photos fast and is great for archiving.
- You can find some great shooting and editing tips on YouTube. There's tons of idiots out there, so find someone who isn't a knob and stick with them.
- Look at lots of photos for inspiration—especially bad ones.
- The more often you shoot, the more mistakes you will make. That's a good thing.
- Ask for help and constructive criticism from people who's opinion you care about. Ignore everybody else.
P.S. You want to take photos of your cat? Take photos of your cat!