At VIE Marketing, we tend to avoid generic packages as clients (and their competitor environments) are all different. For project based work, we charge an upfront fee as the full scope of the project is known. For ongoing work, we either charge an hourly rate, or arrange a retainer based option. (usually the best value for the client). Our proposals are written from scratch, and itemised so clients can test us out before investing further. We don't charge extra for successful campaigns; we don't require a minimum commitment in terms of contracts/investment. We align with what the client needs!

I know it may not sound overly helpful, but it really does vary by agency.

Ultimately, to get the best results, have a really clear understanding of the outcomes you're looking for. If you know what you're looking to achieve, who you're trying to reach and the problems your business is trying to solve, most agencies will tailor their costs and offering to help you achieve those outcomes. 

The cost itself is usually then determined by the assumed number of hours it will take to achieve the outcomes. The functions being executed will have different costs, as will the experience and seniority of the professionals working on your problem. 

So if you're building a new website, it would look something like:

Designer: 20hrs @ $xxxx per hour = $xxxx
Developer: 15hrs @ $xxxx per hour = $xxxx
....

And so on.

There's also been a shift of late to performance based compensation, which is an appealing prospect as it ties objectives to compensation, but not commonly used:

https://www.contractingbusiness.com/service/performance-based-compensation

It's essentially the process of paying the agency for a specific outcome or paying extra for work that goes above and beyond the normal call of duty.

It largely depends on the agency.

We charge either for a project itself but also offer ongoing services based on monthly retainer.

It depends.  We charge by the project or on a monthly retainer depending on the scope of work but some firms  will bill clients on an hourly basis.  Others may work for a success fee or for stock so you just have to ask, there is no set fee structure for agencies.  Sometimes there is an initial set fee to get started then an ongoing lower fee to maintain support so first figure out what help you need then work with your agency partner to strucure the fees in a way that works for both partiies.  In many cases agencies can be flexible when clients are clear on their objectives and goals.  Good luck.

As my clients have different needs, I chat with them about their needs and then put together a proposal for them. No one size fits all. All my terms and conditions are listed in the proposal document including how many revisions are included (mostly two for copywriting services) and payment terms (50% upfront). 
I offer per project or monthly retainers based on the work. 

Great question. It depends also on what type of agency it is. Usually Digital Creative, SEO, UX etc tend to be more of a fixed price / retainer / hourly. Digital Media agencies tend to work more on a % of media spend. So say a $15K Meta campaign might attract a 10% media managment fee so $1500 as a fee for example.