Edit and convert text brand name to vector file for print

I have to jpg files attached, I'd like to take the file Sanamist_JPG_Edit_Example.jpg and convert it to a vector file, .svg, ai and high res jpeg and png for print. The font is Nearo originally. Some of your design attributes to contribute would be welcome... (Budget: $10 - $30 USD, Jobs: Adobe Illustrator, Graphic Design, Illustrator, Print Design)