Yes you need a preamp, but you already have one (its just not that good)
A good preamp is one of the most important tools in a studio and perhaps one of the most important in the recording input chain. With out a decent preamp you will never get a decent recording since you will start out with a bad signal. Here is the issue in a nut shell:
A microphone turns mechanical waves (sound) into electric signals it does this by means of an element (there are a few different types so we wont go into specifics here) by comparison these signals are weak. Back in the days of magnetic tape it took a signal of some strength to get a track written onto the tape. These signals were of a far greater power than a microphone element could generate. Thus a preamp is needed to fill the gap. The preamp adds power (gain) to the signal so that it can be recorded properly. Over time standards were developed and Preamps became devices that brought signals up to line level (being the standard level for audio signals). When the world moved to digital technology the line level standard carried over and so did pre amps.
Side Note: in theory with sensitive enough tape and good enough cable you dont need a pre amp...
Any way, over time preamps have taken on a life of their own and all have their own characteristics now, some more desirable than others. When home recording/computer interfaces became popular in an effort to have a one stop shop companies integrated 1 or more mic preamps into the interfaces. This allows the basic user access to usually 2 preamps and the ability to use 2 mics at a time. They also have regular line level input for things like drum machines, synths etc. You can also run the output of a mic pre into these line level inputs as well. To save on space and cost most built in preamps are OK at best. They have little color and are often just enough to work. Some of the higher end interfaces have better ones but they are still not great.
Consider a channel strip:
You can buy a lone preamp that is very very good but since you mentioned wanting EQ and Compression as well you may want to look at a channel strip. This will incorporate both the great pre and often the companies EQ and sometimes Compression units in a nice 2U rack space. The prices on these are all over the board but so is all audio equipment.
If you are going to splurge, get a nice channel strip, it will last you a life time. If you dont want to spend quite that much get your self a standalone pre, it will do what you are looking for and you will always be able to add a compressor later on.
I have a focusrite ISA One that is really nice. It provides a lot of connection options and a dedicated headphone output onboard. It is good for both mic work and guitar/bass DI. The onboard analog VU meter is a nice touch as well. It has a clean crisp true sound. This is my go to vocal pre and is always wired into my symetrix compressor which leads to a great vocal track.
I also run a UA Solo610. This is a different beast, it has a great tube warmth and a smooth sound. It lacks a VU meter but has a peek indicator to help out. I use this mainly for recording mic inputs from, guitar amps, bass drums, snares, or any other high pressure input. I have limited time on some horn tracks with it that came out nice as well.