Have logo redrawn in Illustrator

Information for the business: This is for a nonprofit sports club's fundraiser
Industry: Sports and Fitness
Design details: They gave me their 'logo' which i believe was drawn at some point by hand by someone in the club. I need this exact logo but it needs to be redrawn so that the line work can be made thicker or thinner in Illustrator depending on the use. For example, we need to get it printed on shirts, but we may also want to print it on some posters so the lines may be made thinner for that so it doesn't look too heavy.
Target audience: racquet players
Ideas for the visual style: line drawing - do not 'stylize' - this is their logo
Things to avoid: don't try to get fancy, Keep it straightforward
Preferred colors: black with transparent background
Where the design will be used: print signs, embroidery, printed on shirts, etc
Extra notes: i am attaching a photoshop file that's been made transparent i thought i woiuld be able to just trace it myself in illustrator but my Illustrator skills are not very good anymore. This is for a nonprofit so i am paying out of pocket to refine/redraw this.