If your partner's passport bio page will be certified, you do not need to send their long form birth certificate.
The birth certificate is ONLY required if the passport copy is not certified and is just a regular photocopy (the birth certificate is then used to verify the information on the passport, instead of the certification being the verification).
You also do not need to include your bachelor of science degree certificate. You can send it if you want to, but it will not help your application in any way as they are not allowed to consider your employability for the visa... they probably won't even look at it.
My questions are regarding our personal statements. What should we include in them? How long should they be?
You don't send 'personal statements' as such.
Your sponsor must send a letter of support for your application, an example of which you can look at here:
http://www.londonelegance.com/transpondia/sites/default/files/spousal.pdf(And you can read more here about the spousal visa application in general:
http://www.londonelegance.com/transpondia/family-visas/spousal-visa)
As the applicant you do not need to write any statements for the application - all of your information will be on the application form.
If you wish, you can include a cover letter with the application, but it should only state what visa you are applying for, what documents you are including and any important information about your documents (i.e. if you wish to explain a criminal conviction or an unusual transaction on a bank statement), or if you wish to post-date the visa you can highlight that in the cover letter.
Does it look like we are missing anything, other than the application? Also, which Appendix will I be printing out? Can I do this prior to filling out the application?
You need to print out Appendix 2.
I would recommend filling it out before you submit your online application (and getting everything else ready as well) - that way you know everything is ready to go and you won't be stressing yourself out later on trying to get everything to the consulate on time.