There are a number ways to deal with libraries in Altium, and there's not really a right answer. If you're actually making a new library from scratch for every project, though, I don't think that's a good use of your time. Component data including footprints and sch symbols are stored in the projects where they're used, so you never have to worry about losing that information if the project files are separated from your local libraries.
Using the manufacturer part search and the ready-made symbols and footprints you find there can be a fast solution, but then you are relying on those things 1) being correct and 2) having the data and formatting that you want. I would hope that those symbols and footprints would be pretty decent, but it's always a good idea to verify for yourself that everything is correct before using them. If you're working on your own then it's up to you how much to care about how consistent the symbols and footprints are and what level of information you want in them, but if you're working as part of a team then that matters a lot more. Big companies may have dedicated people (or a whole department) to serve as librarians, making sure all of the symbols and footprints are correct and comply with company standards.
Consistency and correctness are especially important with footprint design, because the quality of the footprint directly determines the quality of the fabrication and documentation outputs. The quality of fabrication outputs directly affect the quality and reliability of the finished product--getting the right amount of solder paste onto the board and in the right shape, for example, is critical to preventing bridging and tombstoning.
Consistency is less critical on schematic symbols, and it's easy for engineering types to dismiss the graphic qualities of schematic symbols as irrelevant aesthetic nonsense, but the reality is that creating a good schematic is as much a matter of graphic design as it is engineering. A good schematic is clear, well organized, and easy to read, and makes the most important things most prominent. Having good symbols is an essential part of that. Personally I just plain hate the default graphic style and colors in most Altium sch symbols, so I always create my own. That way I can ensure that fonts and styles are consistent, the relative sizes of components makes sense, etc, which all makes for a better schematic.
However you acquire or create your symbols and footprints, I strongly recommend looking into creating a DbLib for your library. These use a database (which can be an Excel file, an Access database, or a full SQL server or whatever) to link schematic symbols, PCB footprints, and whatever other data you want into a single library. It makes it incredibly easy to reuse sch symbols and footprints and add new components--if I want to add a new resistor value, I can just duplicate one row for a similar part in the database, edit the value, manufacturer part number, whatever, then hit F5 in Altium's component panel and place it in the schematic. There are a number of threads here on how to organize DbLibs if you just do a search.