I’m also a short arse at 5’5″ or 5’6″, depending on heels, and ride a 51cm road bike. My first one was a 54cm and it felt too big. This one feels a little long sometimes but I think that’s just my belly getting in the way, most of the time it feels just right.
Obviously everyone is different so go and sit on as many as you can, but I wouldn’t recommend going above 52cm. Bear in mind that if you’ve never really spent much time on a road bike they’ll all feel too long or stretched out, this is normal so don’t get something too small or you’ll hate it.
I’d recommend going 2nd hand with your budget, but you really need to have a good idea of what you want first. Wether you go new or 2nd hand if you have a friend nearby that rides road ask them to come along and help you when you go looking.
To help you compare, MTBs I’ve owned, ridden, and felt comfy on include:
16″ Kona Cinder Cone (94)
Small Cotic Soul
16″ Orange Five
Medium Specialized Stumpy FSR (2004, 100mm)