In the last decade, autonomous vertical take-off and landing (VTOL) vehicles have become increasingly important as they lower mission costs thanks to their re-usability. However, their development is complex, rendering even the basic experimental validation of the required advanced guidance and control (G & C) algorithms prohibitively time-consuming and costly. In this paper, we present the design of an inexpensive small-scale VTOL platform that can be built from off-the-shelf components for less than 1000 USD. The vehicle design mimics the first stage of a reusable launcher, making it a perfect test-bed for G & C algorithms. To control the vehicle during ascent and descent, we propose a real-time optimization-based G & C algorithm. The key features are a real-time minimum fuel and free-final-time optimal guidance combined with an offset-free tracking model predictive position controller. The vehicle hardware design and the G & C algorithm are experimentally validated both indoors and outdoor, showing reliable operation in a fully autonomous fashion with all computations done on-board and in real-time.