I think Arsenal is quite underwhelming - the grenades are too slow and don't do a lot of damage. I very much prefer Puncturing Arrow even in W build. Not sure about level 7 - I alternate between Searing Attacks, Repeating Arrow and Caltrops while playing Valla in Multishot build. I think Caltrops are better for a new player, and you will figure out your own preference later when you're more comfortable with her

Speaking as someone who prefers Q build over others, for Hungering Arrow build it may sometimes be worth it to take Tumble at level 16. Even while knowing how strong is Blood for Blood is, additional mobility and one more Q can save your life. The main advantages of Q build are its range/safety and surprising burst. Tumble helps with both. I am still not sure for myself which is better by default. Also I like Rain of Vengeance but it is the matter of preference and enemy team composition.

Also consider trying Frost Shot into Executioner for an autoattack build - it is 40% damage and slow in your kit.