I had the same question years ago. I have used http://virtualcantor.com/
I liked the versatility of the site. But also its clarify for newcomers. I did not know the structure of the tefilla and therefore the way portions were broken up in a list of clearly named sound files really helped.
I even found it to be useful in teaching me the amidah for davening at home. I used to need ages to finish davening and I did not become faster by reading everyday. I dreaded the longer parts. Through the website i learned the melodies for the repetition and this gave me a melodic rhythm to help me understand the text. These were steps that helped me reach the level necessary to start as a shaliach tzibbur, but also to understand what skills in hebrew reading i lacked and how to overcome it step by step
The melodies are also a nice combination of melodic yet not too 'professional' for someone who has not been trained to sing. I just started with learning to read by practicing the parts that were sung. Now i can read and understand tefillah and use the melodies that are more traditional in my shul, but for me: it all started with virtual cantor.
In addition, my learning speed and quality have been greatly improved by studying small parts at a time not so much for singing, but so as to study the translation in my siddur. The siddur vocabulary is relatively limited so in the beginning many words were new, but after a short while it becomes easier to learn new parts, because you recognise words. This understanding is the "trick" of improving quickly. It also makes you more versatile: you can read 'surprise' sections easier, such as ad hoc added psalms for unforseen reasons, etc. Not only because you can read words. But understanding makes sure that you can improvise a melody that supports the meaning and syntax of what is written. The websites out there can be a useful crutch, but relying on them is a short road that is long. Complementing practice with understanding is the longer road that is short.
A final note: it is important to understand the basic halachot of the mincha service and tefilla in general. Knowing when to skip or add sections, why and when to kaddish is said and which type, etc. are all things that attribute to fast learning and practice. In the beginning it can be sufficient to have functional knowledge of the texts and melodies said by the chazan, but make sure to incorporate all three elements: singing, textual understanding, and halacha into your learning routine.
edit: given all the different styles and nusach out there, there are more (sometimes similar) weekday-nusach resources, such as wonderfully aggregated by offtonic.com