It really depends on what you want to do.
You'll get iPhoto with the Mac I believe - that will provide basic editing and cataloging facilities (see
https://www.apple.com/uk/mac/iphoto/)
Then you have iPhoto's big brother - Aperture (see
https://www.apple.com/uk/aperture/) about £50.
Both of the above allow you to adjust the image as a whole, with some local adjustments via a system of brushes, Aperture giving you a lot more control, and more options for local adjustment (iPhoto is limited to blemish removal). iPhoto is a simpler interface, Aperture, by necessity, more complex. Both programs work together synergistically.
Then you have Adobe's offerings - there are a number of offerings each with different uses.
Lightroom (
http://www.adobe.com/uk/products/photoshop-lightroom.html) £100 - this is roughly equivalent to Aperture in it's target market. A huge amount of control of the overall image and a healthy set of tools for local adjustment . It appears to be updated more frequently than Aperture, and is a very powerful tool. Like aperture, think of this as your digital darkroom - it's for developing and refining images.
Also from Adobe we have Photoshop Elements (
http://www.adobe.com/uk/products/photoshop-elements.html) £60 and it's bigger brother Photoshop CC (
http://www.adobe.com/uk/products/photoshop.html) approx £20/month - these are designed around 'editing' images - that's to say making structural changes to the contents of photos - moving elements around, combining the elements of multiple pictures into one etc. They are both very powerful tools, Photoshop CC being extremely powerful and somewhat more complex to learn, Elements being aimed more at the starter - but still powerful nonetheless.
Now, this is where is gets a little messy. In terms of editing an image, Photoshop CC can to EVERYTHING Lightroom can do and a lot more, however the interface / workflow within Lightroom is designed to make it easy for you to do the 'development' bit very easily, and for you to manage your photo libraries simply, whereas the interface within Photoshop is focussed more on the editing of a single image.
All of Adobe's offerings come with a 30 day trial - so make sure you download and test to see if they are for you!
Outside of these two there are a number of other tools available - From the 'free' Photoshop CC Equivalent GIMP (
http://www.gimp.org), OnOneSoftware (
http://www.ononesoftware.com) and others. There's a lot to choose from! Perhaps if you could have a play for free with the software above and narrow down what you expect to want to do with the software, someone might be able to give you some more targeted advice.
There's also the software that came with your camera.
On a personal level, I started many years ago with the original version of iPhoto, moving to Aperture when that came out a couple of years later. I moved over to Lightroom when that appeared, and today do probably 90% of the image manipulation within Lightroom. I use it to take my freshly shot images, organise them into folders, tidy up the colours, exposure, contrast, straighten wonky images and touch up minor blemishes or remove small elements from the photo - all of which is easily within Lightroom's capabilities. If I'm taking photos of buildings, I'll use it to straighten some of the verticals, on Landscapes, I might use it to reduce the exposure on the sky to balance the image. Sharpening, cropping, perhaps brightening the eyes etc - all Lightroom.
If I need to make a more drastic change - perhaps remove a distracting parked car in a landscape, combine two photo's to make sure everyone is smiling in a group shot etc, then it's over to Photoshop (elements initially, but I've recently upgraded to Photoshop CC) - but this is relatively infrequent. If I only had Lightroom, it would not be too limiting!