Generally, engineering programs will require a high level of preparation in math and physics / chemistry / biology, depending on what field of engineering you want to go into (chemical vs mechanical vs biomedical, for example).
For IBDP, this could mean HL Math and HL Science(s). Many schools will accept either Math AI HL or Math AA HL, but always check entrance requirements!
For US High School Diploma, this could mean taking AP Calculus AB/BC and AP science courses, or IB certificates (if the country you are considering accepts them). The most selective programs will expect AP Calculus BC / HL Math.
There are many types of engineering degrees, but they broadly break down into:
Chemical: Combines chemistry and biology with general engineering principles. Chemical engineers are responsible for refining production methods and for producing products like chemicals, pharmaceuticals, synthetic products, fuel, or food.
Civil: Designing civil infrastructure that communities rely on for their daily lives, such as bridges, roads and water systems. Civil engineerings might work for the government, a construction firm, or a consulting office.
Electrical: Studying electricity, electronics, and electromagnetism. Focusing on projects related to power generation and distribution, or designing electrical systems in buildings or devices. Electrical engineerings can work in industries such as a power grid provider, a telecommunications network, an electronics company, renewable energy, etc.
Mechanical: Designing mechanical systems like engines and heating / cooling systems. A very broad engineering degree that can equip you for working in many industries like robotics, automotive, or aerospace.
You might also want to consider engineering technology. Engineering technology offers a hands-on, applied approach to engineering. Engineering technology students spend more time working with their hands and physically building things. On the other hand, engineering is highly theoretical and relies more on high level math and physics. Engineering students spend more time designing things. Engineering technology degrees can still lead to careers in engineering.
Resources for engineering in the US
ABET is a fantastic resource for rigorous, highly respected engineering and engineering technology degrees. An ABET accredited degree is the gold standard for engineering.
If you are interested in a liberal arts college environment, not all liberal arts colleges offer an engineering degree. However, it is common for liberal arts colleges to offer a "3+2" program for engineering. Students spend the first three years at the liberal arts college pursuing a related degree like mathematics or physics. Then they transfer to a larger research university for two years to get an engineering degree. In five years, students complete two degrees. Many liberal arts colleges are partners with research universities like CalTech, Columbia, Dartmouth, WashU, etc.