For this answer, I have assumed that you prefer open source solutions to big data visualization. This assumption is based on budgetary details from your question. However, there is one exclusion to this - below I will add a reference to one commercial product, which I believe might be beneficial in your case (provided that you could afford that). I also assume that browser-based solutions are acceptable (I would even prefer them, unless you have specific contradictory requirements).
Therefore, I would recommend you to take a look at the following open source projects for big data visualization, which are powerful and flexible enough, but operate at a higher level of abstraction (some of them are based on D3.js foundation and sometimes are referred to as D3.js visualization stack).
- Bokeh - Python-based interactive visualization library, which supports big data and streaming data: http://bokeh.pydata.org
- NodeBox - unique rapid data visualization system (not browser-based, but multi-language and multi-platform), based on generative design and visual functional programming: https://www.nodebox.net
- Processing - complete software development system with its own programming language, libraries, plug-ins, etc., oriented to visual content: https://www.processing.org (allows executing Processing programs in a browser via http://processingjs.org)
- bigvis - an R package for big data exploratory analysis (not a visualization library per se, but could be useful to process large data sets /aggregating, smoothing/ prior to visualization, using various R graphics options): https://github.com/hadley/bigvis
- prefuse - Java-based interactive visualization library: http://prefuse.org
- Lumify - big data integration, analysis and visualization platform (interesting feature: supports Semantic Web): http://lumify.io
Separately, I'd like to mention two open source big data analysis and visualization projects, focused on graph/network data (with some support for streaming data of that type): Cytoscape and Gephi. If you are interested in some other, more specific (maps support, etc.) or commercial (basic free tiers), projects and products, please see this awesome compilation, which I thoroughly curated to come up with the main list above and analyzed: http://blog.profitbricks.com/39-data-visualization-tools-for-big-data.
Finally, as I promised in the beginning, Zoomdata - a commercial product, which I thought you might want to take a look at: http://www.zoomdata.com. The reason I made an exclusion for it from my open source software compilation is due to its built-in support for big data platforms. In particular, Zoomdata provides data connectors for Cloudera Impala, Amazon Redshift, MongoDB, Spark and Hadoop, plus search engines, major database engines and streaming data.
Disclaimer: I have no affiliation with Zoomdata whatsoever - I was just impressed by their range of connectivity options (which might cost you dearly, but that's another aspect of this topic's analysis).