Suggested mouthpiece for new (used) Yamaha YSL 354?

My son's a flute and sax player, but to have a shot at making the jazz band as a freshmen next year his teacher said he really needs trombone players and should try it, so I just bought him a Yamaha, but it doesn't have a mouthpiece. Would you advise against something 2nd hand, or what's a budget-friendly option, if any for a new one? Thank you! I see cheap things like this but i have no idea if it's good/compatible: https://www.ebay.com/itm/127868203593?_skw=mouthpiece+small+shank&itmmeta=01KTT7YVHR2TW75VPBR7FE43PE&hash=item1dc589f249:g:kSAAAeSwkxNqCIdk&itmprp=enc%3AAQALAAAA8GfYFPkwiKCW4ZNSs2u11xA%2F4Ks1eAP%2FVRhZzRVOcFYOOfV%2FUcDdyZ93BS6iJGw%2FnxIq3rsCeSdFajUIAcnidEFRJmULXgwDcOPYo0jVeg5oFaa26vCjzvfLmoPeuO24fQrArNBWVzuaLR35uVr7870cKW3m9sXRS9bNemNwrp1syMLsCDWWtoNpxPM9ka4T1adUBU17hSYYN%2BlnF3g%2FC30W7nX622f8mDB06XW9qxr20bfWLA4ZF3jkBn24YjhUpVx3vajgp1F3ZYkN%2FGx4dXvbCmw9aWLY03oHc0yhzEbvRA7WpC1OfjYxNv4IC1TEtA%3D%3D%7Ctkp%3ABFBMhrn7x9Zn