Help sharpening and brightening this image

If you're doing this as paths, as above, you are definitely making it vector. However, I'm not sure we're seeing everything we should be seeing to make a determination. Would you please show us your Layers panel as well? And, the settings on your pen tool? I just tried it on your very low-rez original post's image, and it's coming out cleanly for me (considering I'm at 500% zoom). Here's a screenshot of my pen tool settings and my window with layers:

I used the pen tool around the letter and S in the name of the logo with the plan to make this all vector and now I can't seem to get the stroke color to show up. Can someone help me figure out what the problem is? I made a new layer and every time I select the S it says there is nothing on the layer and stroke can't me done.

To address your overly bright areas of the image, you may find that excluding the brightness/contrast and levels, and doing it all in Curves may be a better choice. In Brightness/Contrast, you really only have the choice of more or less. If you lighten the image, you're bound to clip some of the more subtle detail in the highlights. Similarly, with Levels, you only really have control over the lightest, darkest and middle range pixels - so if you move the highlight slider inwards, you're again going to clip away some detail in the highlights.

With Curves, you can choose to brighten only certain ranges of tones - and if you watch to make sure the white point doesn't get moved (or that the curve doesn't touch a side), you can retain quite a bit of the detail in that area, while still brightening the light parts.

Sometimes, I'll even make multiple curves adjustment layers with masks, so that different areas can have different amounts of adjustment.

As for the uglification of the pixels on that logo - it appears the client stole it from his/her own website to put it into print. I see this all the time. They let their "original designer" keep the image, and just have their website copy (low resolution, compressed). They'd want to get the original from whoever has it. OR,  you can tell them you'll fix it - recreate it, and then make more money?

If you have InDesign and you create this in it, you'll get a much better and more professional output.

For sharpening the image (i.e. the photograph) you can use Clarity in the Camera raw filter which uses local contrast to give the impression of sharpness and also the sharpen tool. Don't overdo it though - over-sharpening looks awful.

For the logo and text  - you need to obtain a vector version of the logo, or recreate it using text layers where you can find the font and as vector drawing for the tap and "Superior" element.

Dave