The Scarlett has a pre amp built into it. Most likely the issue is the distance you have the microphone from your mouth. An SM57 is not ideal for podcast recording because you will need the microphone inches from your mouth, as well as dealing with proximity effect. You would benefit more from a condenser microphone than an external preamp.
I'm a little late to this discussion. Thought you might want to look into Focusrite as well. I've had very good experiences with their equipment. I think their Scarlett series is in your pricepoint. I'm not sure who you would use locally (New Zealand?) but here's a link from a retailer I've used a lot.
Another option is a hybrid. Digitally controlled, but ...
What you need is a USB sound interface with four or more inputs. I tend to search in specialized sound internet seller to see what is available on the market. One example is https://thomann.de in Europe or https://www.bhphotovideo.com in the USA. Once I see what is available next step is to visit the manufacturer web site and read the manual. It sometimes ...
Yes the three items will work together.
You are correct, a turntable needs a pre-amp or a "phono stage".
Before CD's changed the market place all (most) stereos, Pre-amps or integrated amps had a phono stage built into them so all you had to do was plug your turntable into the Phono RCA inputs on the back of the unit.
Now only higher end components ...
Just rang Rode directly as I needed an answer myself.
SmartLav+ = you use the Rode SC3 adaptor. The VXLR+ adaptor that someone linked here is for the traditional lav microphones that have a TRS connection already.
Hope that helps.