Andrew,
There are many different routes to Nirvana
I'm a PixInsight weenie. I have tried several of the other options and PI is what works for me. It does have a steep learning curve and probably suits the hardcore geek best. You can get a time limited evaluation version to try for free. Check out the Harry's Astroshed videos if you are interested.
CCDStack is another nice package. It is quite a bit easier to use than PI but (IMHO) less powerful. I think you can get a free eval of this as well. Adam Block has some nice instructional videos but you have to buy them.
Hardcore Photoshop users also produce some great stuff but I think you'd be silly to take this option unless you already have a lot of time invested in Photoshop and are a guru. Forget Lightroom. It doesn't really have anything to offer for astro image processing.
You can also get by with DeepSkyStacker and free tools but I think if you're serious you'll need to upgrade at some stage.
That's my $0.05c worth!
Cheers,
Rick.