Is the number of contacts or memberships we can manage for free limited ? I don't see this information on your website.
CiviCRM is a free, open source software package. You can download it for free, and you can do what you like with it.
The number of contacts or memberships supported is not limited by licensing or restricted in any way. Practically speaking, the limit will be what your website hosting can support.
For most cases this is effectively unlimited - some CiviCRM sites have millions of contacts. Organisations of that size tend to spend more on hosting than smaller orgs. Your mileage will vary according to your needs. I know of sites running some thousands of contacts on "commodity" website hosting. While this works, it can be more work (and cost) than using a provider familiar with CiviCRM.
Getting up and running is the first step, but in future you'll likely need help keeping your site running well, ensuring your contact data is secured appropriately when updates are released, and configuring or customising the features your org needs.
You'll find there is a great community supporting CiviCRM and its users, with places like the forum and IRC. If your org has technical skills "in house" you'll probably be able to get up and running by yourselves. Even so, find some allies to help you on your way. You might find some orgs in your space or existing network who are using CiviCRM, and there are a range of commercial outfits supporting CiviCRM as well.