Company Logo

I have a logo for my company though I have gotten to the point where a .png doesn't serve my needs any more as I am needing to do larger prints and would like a vector image remake of my logo. I have .png file and .jpg file of this logo as well as all the color codes I would like to use. I am not looking for a rebrand as I am happy with my logo and my customers have just started to recognize it and associate it with my company. Should be a easy thing I just don't have the know how or tools to do it. Color codes are as follows: Red #ea0406, Black#181818, and the white is true white (#ffffff I believe) regardless of the included image named Logo_With_Oval.png (in that image the oval is #ece9e0 or something, it is an old design and no longer used with that color the oval will just have a color change to that true white I mentioned earlier). I would like two vector images one that has the white oval in the background and one without.