Hello everyone!
My name is Pedro and I’m new to the forum.
I’ve recently enrolled a Classical Studies program and I’m trying to catch up on some culture, history and literature (my background is Philosophy). I’m counting on you all to help me with some reading suggestions. Right now I’m looking for good overviews on Greek and Roman Histories (I know they span over several centuries, so I’m okay with books that focus on certain periods).
Thank you all! 
Welcome to Textkit, Pedro!
Thank you so much Bedwere! Can’t wait to work and discuss with you all 
On Greek history you could look at this thread:
http://discourse.textkit.com/t/ancient-greek-history-text/18966/1
An old fashioned but standard textbook on Roman history is: From the Gracchi to Nero: A History of Rome 133 BC to AD 68 by H. H. Scullard
A short introduction is SPQR: A History of Ancient Rome by Mary Beard.
There are lots of suitable texts perhaps your tutors can provide a reading list?
I agree, great choice.
Here are two more recommendations:
Roman Realities by Finley Hooper (covers the republic, principate and dominate; expertly written, good prose, a fun read; around 500 pages)
The Roman Republic: A very short introduction by David M. Gwynn (concisely written, under 150 pages)