When you choose a project management software, you have to consider a lot of criteria, such as features and cost. If you are a startup, you definitely want to maximize your ROI on project management software. With a lot of project management software available, it might be very difficult for you to make your decision. You can start with pricing comparison.
Jira has Cloud and Self-hosted versions. It is well-known project management software and the "big brother" in this industry. Its cloud price for up to 10 users is $10 per month, which is quite reasonable for startups.
However, the cost of private deployment is expensive, if your team has more than 10 users. You might start to think about alternatives. There is some project management software that is free and open source .
Trello is from the same company which owns Jira. It has free version and enterprise one as well. If information security is one of your concerns, it might be better not just using it because of free.
ZenTao has cloud and private deployment. Its cloud service is quite competitive. You only pay $199 a year for an unlimited number of users, which is so much economical and practical. Meanwhile, its features are comprehensive. ZenTao Cloud covers the whole process of software development.
Basecamp is not just a project management software. It has a community that guides you through project management. They have books that you can buy. One of their famous publications is Rework. However, it is not cheap when it comes to price.
I love their designs, btw *-*
Asana adopts kanban too. Since we are not going to discuss features here. Let us just go straight to pricing. Asana has a free version which covers the very basic features of a project management software. Its business version is charged by user monthly, which is a little bit expensive.