Nice pics. I run AV mode (Cannon) or A mode (Nikon) with the lowest F-Stop that the lens allows. Also position yourself so that you are using just a little under the full zoom capabilities of the lens you have, make sure you have the subject you are focusing on taking up most of the shot. This will work best to get your backgrounds out of focus. A basic quality 18-55mm lens will not really do that well for this. I love my 55-250mm lens and use it for almost everything. It's the best all around zoom.
Depending on lighting I try to run lowest possible ISO, this will give you best quality pics, but also reduce shutter speed. During a bright sunny day it should be fine. If they start getting blurry start stepping up the ISO. When you are in AV or A mode the shutter speed is, by default, on auto. These are the settings that I almost always use and are great for when you are new to photography.
I only use manual mode when I am getting creative with filters, long exposures, HDR images, etc.
As far as software, Lightroom is the best for editing your photos. The best way to describe it is Instagram on steroids. You can go online and download tons of different filters that other people have created, and add your own touches to them too.
Photoshop is more for serious editing of the picture. Removing/adding objects into the picture, placing objects on different backgrounds, stretching/shrinking things, etc.
IMO Lightroom is the best for making your pictures look nice. If I have a good shot but something is in the way or I want to get more creative then I use Photoshop.
Photography has been a hobby of mine for a long time. This reminds me! I need to get some good pictures of my bike before the snow flies.