Niels van Reijmersdal and Dhiman already mentioned the most important point. I'd like to give a look into my experience as my situation was quite similar to yours now some years ago.
I'm on a small freetime project (a browser game) and in the past years we tried to build up at a QA too which is a bit more problematic with only users who do the "work" in their freetime and are not teached into testing / QA. We also tried several ways to handle our issues from sheets over different issue trackers (sheets [excle and google], self written php/mysql page, mantis bugtracker, redmine). In this post I will also havbe a look into JIRA (was used in my university bachelor project first) and HP QC/ALM (we use in the company I work for).
Sheets / self written small PHP/MySQL-"Tracker"
The first things we tried was using sheets and a small webpage for tracking open issues. For the beginning it was okay just to collect the issues and have a list of it. As you we used several colors to identify the status of issues. The advantages are clear: No / Low cost and available to all without real work. But quite fast we moved away from this for the following reasons:
- Not much space for descriptions <-> Loosing track of the issues due heavy descriptions. Always moving the cells to show / hide the descriptions and so on or have several related documents to see the details
- No history of issues. That was the most important point why we moved away. We could'nt track the history of an issue
- Bad search to e.g. look if a bug already tracked
- No syncronisation (at the beginning, using excle sheets)
- No privilidges for different users to change status etc. (Everyone could edit anything)
- No work flow "restrictions" (Even if we had a defined workflow you could change the status as you wanted and skip phases, e.g. by changing the fields to "Closed" and noone would notice.
So I would advise you too use an issue tracker instead of sheets.
Issue trackers
We then moved to mantis bugtracker. It was a huge step for us to have a good look at the tickets, privilidges to seperate at least some actions to different users. We could define a small work flow for issue status. But after some time one of us got in contact with redmine and two people (one QA at his work, one learned software engineer) tried it in a test instance. After only a few hours we know that we want to change because we could define the workflow, user groups and priviledges very detailed. We could define own fields, integrate version control, had a better handling (e.g. changig the status of multiple tickets at once) and much more. As there was also an import plugin to import from mantis to redmine we could take over our tracked issues. Okay we got some trouble because we moved from ISO to UTF8 and the status could not be exactly transmuted but it was quite good and saved us to import the issues manually.
The comparison between JIRA and redmine is like two people arguing about the car they want to drive. The one wants a green car type A while the other one wants a blue car type B. What I want to say this this: The difference between them isn't huge. But for my personal I like redmine more as I think keeping track of issues is much easier and the administration and workflow definitons too - or short I think redmine is more powerful. I got in contact with JIRA at my university bachelor project and we had the problem that I was the 11th person in our team. But JIRA had only 10 free license at this point (some years ago, maybe changed). So I showed the team manager and one of the JIRA administrator our redmine project and hold a presentation what they could to with redmine - there were some points they had problems with in JIRA which they could do in redmine easily but I don't remember them, sorry. After the presentation the admin installed redmine, moved the issues from JIRA to it and we used redmine from them on and could save the money for further licenses.
As already said there are no huge differeces but I think redmine is more flexible and it's free of charge regardless how many users you have. You wrote in your question that you already have JIRA so you I assume you have a server for it. Then you would also have a server for redmine and no need to spend money for it. I don't know how large your team is but if it will grow you may get in trouble with JIRA licenses.
If you would be open source (what I don't think as you spoke about company) github with the build in issue tracker would be a free alternative too, but it is not so powerfull like JIRA or redmine.
A side note on HP QC/ALM. As it's quite expensive it won't come into focus at all but in my experience it can only plays its strenght if you use all aspects (requirements, issue tracking, testing) of it. Just for the issue tracking I really don't like it because of the handling. I don't think this would be a viable investment for you.
Conclusion
Yeah this answer sounds like a payed commercial for redmine but it's just a short summary of my experience keeping issues tracked in small teams with no or limited money. If you are happy with JIRA use it. But if I understand your comments right you are in testing phase at this moment. May you could give redmine another try to have a look on which tool is better suited for you - maybe you don't see a difference at the beginning / all but I think this comes with the detailed requirement of your team to the tool. Would probably to broad for this here, e.g. on my freetime game we don't use the "expected time effort" tracking of redmine but in my university we had to.
But I would emphasize the posts of Niels van Reijmersdal and Dhiman that you should use a tracking tool instead of spreadsheets.