I think you are doing OK. I really like one of the cat photos.
I also think others are pretty reasonable. I will use one to address some of the things you said. (Clicking on photos here will take you to the Flickr file)
Here is an edited version of your photo:
I thought she looked a little too bright so I pulled back on the exposure a bit. I thought since her face is turned slightly to the left side of the photo she may look better on the right side. And, I sized the photo for display on a monitor, to 900 by 600 px then applied some sharpening (more about sharpness below). I think her eyes are a little strange. To me, her right eye is looking right at the camera, and her left eye is focused some place else. Also, her left eye’s iris looks odd. Somewhere on here, we have an eye doctor. Perhaps later he will stop by and tell us I am crazy …
I get a little frustrated with my photos because I’m not always sure whether it’s my cheaper lenses or me causing the lack of sharpness.
Sometimes a lens is not as sharp as we may like. I have returned lenses because they were not sharp. Reading through various forums, I see I am not the only one who has done that. Get a tripod, or a table. Put a page or two of your local newspaper on the wall, held flat with some tape. Light the paper well. Shoot it with each lens, at various focal lengths for your zoom lenses, and at various apertures. Look at the results. You will know if it is your lenses, or something else.
Your camera’s sensor has a filter that is designed to remove sharpness. It is your job to put the sharpness back in, and there are several sharpening methods to do that. Research them, see which ones appeal to you. Some sharpening methods are complex and others are pretty simple. I find the simple ones work well enough for me. When posting or printing, size the photo to the correct dimensions, then apply sharpening to taste. Resizing affects sharpness, so sharpening should be one of the final steps. Posting to any of the on-line forums results in too large images being resized to fit, it is better to choose the correct size and adjust the image yourself than to let their automated process do it.
Focus and blur also affect the appearance of sharpness. Sharpening does not fix either of these things. For portraits, focus on the near eye. Choose a fast enough shutter speed to freeze motion and learn to pan for those times when you want some motion blur but need your subject to be sharp. Image stabilization, a good grip and a good tripod can all help.
Whether you believe in it or not, I try not to be the type of photographer who takes 1000 photos and uses 3. I like learning how to be consistent, not accidental.
Being consistent is good. Sometimes accidents are good too. Getting the photo is the first step. Editing is usually necessary. You should see the effect dodging and burning had on Ansel Adam’s prints. A straight print looked nothing like his production prints! I grew up with Time, Life and National Geographic magazines. You would not believe how many photos were taken, by experienced photographers, to get the few photos you see in the magazine. One photographer took 2,500 photos, and 4 were used. Another took over 30,000 which resulted in 40 being in the article. Don’t worry about taking enough photos to thoroughly explore your subject.