With the present trend towards the use of microservices instead of monolithic software, future applications with diverse computational and delay-sensitive requirements, such as virtual reality (VR) or holographic communications (HC), will be redesigned based on loosely coupled microservices due to their more efficient deployment according to available resources. However, it remains a big challenge to provide such services under stringent quality of service (QoS) requirements at minimum time and cost and with an efficient utilization of the network. Presently, multi-access edge computing (MEC) has been proposed as a promising alternative to deploy future microservice-based applications to achieve faster response times while reducing the overall network load. However, network conditions, edge nodes state and service requests are dynamic, increasing the difficulty for the provisioning of services by MECs. In this context, we propose an optimization deployment heuristic (ODA) to obtain sub-optimal deployments in reasonable time, meeting the requirements of some representative future applications under study. In particular, according to latency requirements, there will be delay-tolerant and delay-sensitive applications, playing a major role regarding the alternatives for the deployment onto single or multiple MEC systems. The evaluation analysis shows that our proposal performs significantly better than other benchmark solutions in most of the metrics used for the experiments, especially in minimizing deployment costs in minimal time.