First project. Automotive. Right direction?

I'm sure there are lots of threads out there with similar questions, but after a few hours of searching I am now even more confused than before. I'm mainly looking for hardware recommendations. I'll figure out the coding side myself.

This is my first arduino project (actually my first real electronic project).
I've made a couple of ROVs before using DPDT relays, and I've coded in Java and VB before.

I want to start small. I want to be able to detect the RPM signal on my car, and then have it control a few outputs based on this (relays to turn on a light, etc). Most of the searches I did involved pulling data from the OBD-II port, but I will be using the wire that comes straight from the PCM and normally goes to a Tachometer. I will not be using a tach other than Arduino.

My hardware requirements:
-Can read signal for Tach.
-Has output for an LCD screen to display RPM (Probably 40-pin).
-Can control relays

Optional:
-Can read 0-5v inputs
-Can also Read Speedometer signal

If anyone can point me in the direction of what hardware I need to get started, that would be great.
Also, a link to a page that describes the different types of hardware available would excellent as well.

I know it probably seems like I'm asking to be fed from a big spoon for those of you that answer these questions far too often, but thanks for being patient with me.

The first thing you need to do is determine the voltage of the device you are planning to read from. I'd guess 12V+, since it is automotive. Feeding that into an Arduino will result in some magic smoke escaping, never to be seen again.

I believe the Tach signal is 5v square wave, as most are required to use a 1k Ohm resistor and add a 12v signal to get aftermarket Tachs to work correctly.

It looks like I may pick up the Arduino Leonardo with Headers.
It fills the needs of ~10 possible analog inputs and ~5 Digital Outputs with at least a couple of PWM outputs.
Its also USB Native which helps.

I would still need to solve the issue of the 40-pin Display. I keep seeing the RA8875.
Would I be able to use the RA8875 with The Leonardo with headers and keep roughly 10 analog inputs, 4 digital outputs and 1 PWM output? I’ve thought about jumping straight to the Due, but I wanted something comparable in size to the 7" screen.

Since you are going to be working in the automotive environment, you need to address the issue of not only power supply regulation but signal conditioning on all inputs to the Arduino - the automotive environment can be very harsh with spikes and all sorts of odd things happening (depending on where you ground things, you can even find that ground in one place is several volts different than the ground in another place - especially when you start the engine (the starter pulls lots of amps). You need to verify what the signal to the tach looks like then provide signal conditioning from that to the arduino (you also need to make sure your circuit does not load the input the to tach so that it does not work correctly). Typically a low pass filter (RC) helps on the inputs as well as protection diodes or voltage dividers as necessary to prevent the signals from going outside the ratings of the Arduino inputs.

It fills the needs of ~10 possible analog inputs

A Leonardo does NOT have 10 analog inputs. It has 6, just like the UNO and other 328-based Arduinos.

Would I be able to use the RA8875 with The Leonardo

The Leonardo has 20 pins. It seems highly unlikely that you can connect anything which needs 40 pins to it, successfully. The RA8875 (which I had to google; you should have provided a link) is an SPI device that goes between the Arduino and the TFT. SPI uses three pins plus a chip select pin.

I picked up a LOT of different things to help with the learning curve.

I bought 2 Uno R3s, a Leonardo, a Due, and a Mega.
I also picked up about 40 different sensors, a couple of breadboards, a ton of jumper wires, a few different LCDs, and a box of LEDs. I have about a $500 budget for Arduino related projects and I've only spent maybe $200.

I think I should be fine with the automotive analog inputs, as they are only 0-5v signals. I've been datalogging them for years and they do not go over 5v, ever, otherwise the engine just wouldn't run.

The goal is to use something like this for a screen:

I had been suggested this by a local to work with it:

I may try to upgrade to a touch screen at a later point in time.

My next dead end is relay control. I need to be able to control automotive relays, or at least high amp relays. Obviously there are tons of 5v relays out there ready to go for Arduino. I just need to find ones that allow me to pass 12v at up to 15 amps through them. I'm sure there is something out the readily available for this.

EDIT: 4-channel relay module on the way. Instead of passing high current through it, I can use it to control the low-amp 12v signals for existing relays.