Step 1: Understand disaccharides.
A disaccharide is made of two simple sugar units joined by a glycosidic link. Different disaccharides use different sugar pairs.
Step 2: Look at sucrose.
Sucrose (table sugar) is built from one glucose unit and one fructose unit.
Step 3: Check the forms in sucrose.
In sucrose the glucose is the $\alpha$-D form and the fructose is the $\beta$-D form, joined by an $\alpha,\beta$ linkage. So Statement I is correct.
Step 4: Look at lactose.
Lactose (milk sugar) is built from one galactose unit and one glucose unit.
Step 5: Check the forms in lactose.
In lactose the galactose is the $\beta$-D form and the glucose is the $\beta$-D form. So Statement II is correct.
Step 6: Combine the results.
Both Statement I and Statement II describe the sugars correctly.
Step 7: State the final answer.
The correct choice is:
\[ \boxed{\text{Both Statement I and Statement II are correct.}} \]