I'm often asked by students about which music instruments and equipment to buy, so here are some tried and tested recommendations. All suggestions are based on my personal experience, and I would advise where possible to try instruments and amps out yourself in a music shop and trust your own ears and intuition to judge what sounds and feels right for you.
I bought my blue Aria Elecord in the early 00s in a shop on Charing Cross Road, and it's still working well over 2 decades later. It's earned its keep many times over as my busking guitar in London for 2 years, when I probably made its value every week!
My other guitars include Crafter and Fender electro acoustics, a Fender 12 string, an Epiphone, a Gretsch and a Hofner violin bass, plus other instruments, including a mandolin, guitalele, a dulcimer, an autoharp, a bouzouki, ukuleles, a baritone ukulele, a violin, a viola and a cello
(NB 1/2 or 3/4 size acoustic guitars are good for young beginners with smaller hands)
I have a couple of Mahalo ukuleles, a basic model and an electro acoustic. They're great little instruments, durable and fun to play.
TUNERS, CAPOS AND STRINGS
A capo tuner is a great all-in-one option, which means you can tune up and also change the key of any song by clipping it on any fret.
A good tip is to check your tuning again once you put the capo on, as using a capo can affect pitching. This is particularly important when recording or playing live. Check you're tuning to the correct pitch - eg capo 2 would meaning tuning to F#, B, E, A, C# and F#. The Chromatic setting on the tuner will help with this.
Alternatively, you may prefer to have a separate capo and tuner, especially as the 2-in-1 capo tuner can be a little bulky and some find it gets in the way of left hand fretting.
I have both a Yamaha and a Casio keyboard that have lasted many years, so I believe these makes are reliable, along with Roland keyboards, which tend to be more expensive.
It's worth trying out mics in a shop to see what works best for your voice, as different timbres of voice are enhanced by different microphones.
I have an Audio Technika MB1K mic that is inexpensive and seems to warm up my voice more than the more commonly used Shure mics, and I'm thinking of trying the slightly more expensive MB3K too.
You'll find the SM58 in many venues, and it's good to have your own mic if you plan to go out gigging.
For recording, I use an SE Z3300a mic, which I've found works well for my voice compared to many more expensive mics. It came with studio extras including a sounds baffle for less than £200 a few years back. I'm not sure if they're produced anymore, but you may find one on ebay, for example.
I busked for 2 years on London Underground 2003-2005 using the Peavey solo portable sound system. It has an XLR input for the mic and a 1/4" jack input for a guitar, keyboard or other instrument. You can plug it into a socket or use 8 batteries. I used rechargeable ones as this was more economical in the long term.
I also have a Bose L1 PA system for gigs, into which you can plug a mic and instrument, or you can plug in a mixer to it's stereo input for more channels.
1/4 jack to 1/4" jack are used for most instruments like guitars and keyboards for example, and mics are connected by XLR at the microphone end and either 1/4" jack or another XLR depending on the input on the amp.
Here are some books for inspiration. The Frustrated Songwriter's Handbook by Karl Coryat and Nicholas Dobson and The Art Of Songwriting by Ed Bell are full of tips and ideas to spark your imagination and Songwriters On Songwriting by Paulm Zollo contains a multitude of first hand accounts of how a vast array of world famous songwriters create their songs... enjoy!