Should I use existing free platform templates, like PHP, Joomla, or should I develop my own?
It depends on your technical ability. Are you a proficient coder in PHP, Javascript, HTML? If not, learning as you go along in a serious venture such as this may not be the best idea (it will extend the time and overall cost of the project). It also depends on if these platforms offer the services you want - if they don't you may have to get someone else in to create it themselves, again increasing the overall cost of a project.
What are the advantages/disadvantages of either option?
Hand-Coding Advantages/Disadvantages
The advantages of hand-coding include its simplicity and practicality. Hand-coding your website does not require any special
or costly software, and your system’s default text editor will suffice. Also, because you are inputting the code yourself, no additional and unnecessary code will be added. This could lead to a lighter, faster-loading site that is always favorable to the end user. Again, it all depends on your level of coding ability as you may only be comfortable coding HTML but not PHP etc.
The disadvantages of hand-coding are that it requires patience and a broad skill in HTML. It is also a very time-consuming and arduous task — for example, adding an image that could only take you a few seconds in a WYSIWYG editor would require long lines of code that could take minutes to type. A hand-coder must be able to pay attention to detail to ensure that the website will be operational and error-free when displayed.
Platform Templates Advantages/Disadvantages
Template editors are especially helpful with full-scale projects that have time constraints and due dates as they eliminate the need to manually hand-code every aspect of the web page, therefore saving time. WordPress for example is packed with many that can give the user instant effects and designs.
The disadvantages could be that it is more costly (most decent designs cost money) and that depending on how complicated the program will be/where it's hosted, some setup procedures may be slightly complicated for people who aren't used to it. Also, there isn't as much perceived freedom by using templates as opposed to making everything yourself.
As a rough estimate, how much will it cost me to develop and manage my own? And how long will it take.
This is subjective as to exactly what you want, the features you want to implement, the size, the design - so many things need to be taken into account. Always make sure you allow for extensions in terms of time and money as projects rarely ever keep to schedule.
In general what should I be careful about on this journey?
The things that cause the biggest problems in projects are usually bad project planning/procedures, lack of time management, incompatible ideas and lack of knowledge regarding what is actually wanted as the final product.