The least expensive option is to expand into the garage. This is an existing space and does not require foundation work or even a roof. Extensive modifications to walls to install windows and remove garage doors (that can be re-used in a detached). Assuming you have a 2-car garage you are looking at up to 500 square feed that might afford you some relief. If you need to build another garage, this option can spread the cost over more time, but is not a great deal more economical than an addition.
The next option is to build and addition. I prefer this to building up because it is less disruptive to existing spaces, and can be nearly completed before joining the addition to the existing house. A two story addition is especially effective. In this case, utilities can often be extended into the addition and costs for foundation work, framing, roofing and finishing are predictable. If you have space on your lot to build out, this is by far the best way to go.
Building up is contingent on having an adequate footer and first floor framing on the existing structure. This is very disruptive because the downstairs is effectively demolished meaning you have building costs to the existing home in addition to construction and finishing costs of the addition. So this is the highest cost per square foot option in most cases.
For highest return on your investment, be sure to permit the new space and conform in quality to the existing house. A sun room will add little value compared to a conventionally constructed bedroom and bath or other living space. For example, building on a new master suite or kitchen that is high quality will add considerable value to your home. Building into the garage is less desirable because an attached garage has intrinsic value and such additions are often poorly executed from an architectural point of view.