Hiya Chatty.
With those putters you shouldn't be seeing much different in swing speed at all. Although, I stepped up to an Anser putter after my starters and bought balls as well. So not a lot of experience in changing over starter gear.
Balls are the single most effective thing to slow your putting meter down.
Look for balls with a 'Feel' rating. The stronger the 'feel' the more they will slow the meter down for ALL clubs.
the GI series of WGT balls are good value GI2-S / GI3-S
Looking at your bag, you are probably best off seeing new wedges firstly, then a driver.
the wedges will put you closer to the pin and hopefully leave you shorter putting distances.
Level 39 will open up the ATV wedges for you and they will see you good for a long time.