You have several things going on.
You have to remember that PageRank is a trust network scheme/mechanism that applies across the internet between sites and on your site itself. Both must exist. Without both, determining what pages are important would be incomplete.
First, navigational links from the header are typically static and somewhat shallow. For example, "mens wear", "womens wear", etc. Once you get to that page, side bar links could further narrow down shorts, pants, shirts, etc. This is just an example.
Some sites will make their navigation deeper. You have seen this and this is fine unless it gets too involved. What you put into your navigation is up to you. A separate navigation in a side bar works, however, the first navigation found, typically the header, is taken as more important than a side bar navigation. Keep this in mind.
Second, the notion of internal links not effecting PageRank is not completely true. PageRank is also separately applied internally to a site. The home page is where search engines start. Links from the home page are seen as more important. As well, the further away a page is from the home page in terms of links diminishes the pages importance.
The number of times a page is linked to also adds importance. As with navigation, if all pages link to a page, the importance of that page is considered very important.
PageRank + the importance of a page as signaled by link structure is combined as part of signalling importance, however, enough inbound links (linked from another site to yours) to any single page can easily override any internal linking signal. With this is the presumption of the inbound link value and quality and the PR of the linking page. The PageRank passed from any inbound link is a significant signal assuming the link is of value and quality.
Some things are understood as traditional. For example, navigational links. It is okay to have navigational links and even more than one set of navigational links. If, for example, your header navigational links do not change, however, your side bar links do based upon what page you are on, this follows tradition. If your header links change based up which page you are on, this is not traditional.
Link quality and relevance is important. The more descriptive from a linguistics point of view, the better. The more relevant the better. This is just a given for navigation. For example, "men's pants" is clear. "Men's dress pants" is more clear. "Men's dress pants" offers more linguistic signals in terms of term and topic scores than just "men's pants". If "men's dress pants" is linked from "men's pants" the relevance score increases. But please do understand if your site is about clothing, some relevance will always exist. Just think about how you can signal relevance where you can.
Lastly, sculpting is important for SEO. Some argue it is spam, however, they are dead wrong on this. Sculpting is natural and expected. Yes, be natural. But do not be shy either. Your job is to precisely signal to users and search engines what a page is about and how important it is. Keep in mind that you will have transitional pages that may not seem important from an SEO point of view. I argue, these are important pages. For example, "men's pants" can simply transition a user to a more precise selection such as "dress pants", shorts, casual wear, etc. It may at first seem like this page is content thin, however, it is not from a semantics point of view. On one of my sites, my most important page, other than the home page, is my "articles" page. It score high topically and is found in search more times than not. It also engages users and users often hit that page several times to read articles.
One important lesson in sculpting a site is that you will not get it perfectly right the first time out. This requires thought and testing. Do not be afraid to change your linking program to better optimize your site. I use Google Analytics Behavior Flow to study how people use your site. Engagement is your goal. Page with drop-offs could benefit from more engagement. You can create links, for example, to reduce drop-offs and retain users attention. For pages that do engage users, you can see how you can better engage users. You can use this information to better direct users to the pages that you prefer they see such as ones that convert to purchases and pages that offer a better profit per conversion. This is a normal marketing tactic.
For smaller sites, signalling what pages are important is much simpler. Duh! Right? However, for an e-commerce site, this becomes more complicated. You can have a more involved navigation in the header and in the sidebar as long as you do not get too carried away. A marketing truth is, you offer too many selections, people tend not to select anything. Find that sweet-spot between engagement and encouragement. Use the sidebar as your only dynamic navigation. Follow tradition as you see it on other sites.
Specifically what you do on your site, we cannot advise. However, and hopefully, these guidelines will help. It is up to you to determine what is important and what signals you send.