It's not easy to tell you to go for a technology based on your question. GigaSpaces is certainly up to the job but so is Spring Batch. Quartz is just the scheduling part of your question and not so much the remoting and the distribution of workload.
GigaSpaces is a fully fledged application platform to handle scenario's where parallelism, high throughput and scalability is a factor. Spring Batch can definitely also do the job, but unlike GigaSpaces, it is not an application platform. So you would still need to deploy your application somewhere.
However, GigaSpaces is a commericial product (free version available) but there are other frameworks that can help you such as Storm Project (http://storm-project.net/) and Hazelcast (www.hazelcast.com) also come to mind.
So without clarifying your use case it's hard to give a single answer. It all depends on what exactly you want and how you want to use it, now and in the future.