I have a site with a bunch of products on it, about 1600 to 1700 or so. Each product is a different WordPress post... I would be happy for it just to index my home page and other pages I have on my site. About 4 other pages.
The ideal thing to do here to bring more user exposure to those products is to categorize those 1600+ individual products so that you have fewer pages for people to flip through.
For example, if your product is about fruits, then you're better off having one page for all types of bananas, and one page for all types of apples rather than having the following as their own pages:
An advantage to condensing here is that you can create more well-rounded paragraphs that talk about the fruit in general and that would also please the guest.
I mean if you still want individual pages as well, then include them (and don't let search engines index them since information is almost duplicate), but don't make that the only option because guests don't want to click through dozens of pages to find what they want.
If i submit my site maps for just the pages, and home page, will the negatively affect my SEO ranking?
Think of a sitemap as your sales pitch to search engines. It can learn based on the sitemap what URLs exist on your site. Do realize that search engines can scan other pages on your site available to the public. Just make sure you prevent search engines from indexing any pages that will be close to being duplicate of another page.
The reason I ask is because my "posts" which are lists of products have images, price, and a link to the product. I don't need to have Google index all my posts as there isn't enough content to worry about that on them (Like description, uses, etc. etc..).
Condensing as explained above is the best option for you because from the way you're describing your page (aka your post), users could be clicking until they go blue in the face. (sorry, I don't want to click the next button 1699 times).
Would I be OK just having Google index my home page and pages rather than all my posts to?
You'd want to do better than OK. If you can condense your product pages and add descriptive paragraphs to each set of similar products then you can have those indexed as well and possibly attract the impatient users since they might type in a specific product name in a search engine and click right into your product page from search results.