What DAW should I buy?

I'm an aspiring artist looking to compose in an alternative/indie style. I've been using Garageband on my iPhone for some time now, and it no longer accommodates my needs, specifically because my soundscapes are far too large and not simple enough for a shoddy (but reliable) phone program. I use synthesizers the most, but will play with acoustic and electric guitars sometimes, so different effects and sounds are very important to me.

Budget will not be a big problem--as long as it's not outrageous!

Try Tracktion; a full unrestricted version from a couple of years ago is totally free:

There's an article on it in the latest Computer Music magazine, plus there are lots of tutorials on youtube.

I've used it since version 3 or 4, up to the recent version 8. (9 is due out).
The latest (paid for) version is not that expensive. From past history, they will probably make T7 free a few weeks after T9 is released.

On its own, it allows live recording recording of audio or MIDI, importing audio files, MIDI files or samples to tracks.
Using VST plugins you can create tracks totally from synths, sequencers & samplers etc. With any instruments you like.

There are thousands of free VST instrument and effect plugins available online.
eg. One of many library sites:

You need a decent USB Audio MIDI interface if you want to record live audio from a microphone or instrument.
A Focusrite Scarlett (eg. 2i2 or 2i4) is a good choice.

For MIDI only you can use one the the basic USB MIDI interfaces sold for around 5- on ebay, they are fine.

My setup below