I found a job posting on LinkedIn. The post stated that they were looking to hire a virtual assistant. As a University College Student, I of course, thought this would be the perfect job for me during this stage in my life. The employer stated that all that you needed to do was to send your resume to them in an email and they would establish the best person best fit for the position from there. I submitted my resume to the email address as instructed. Two days later I received an email with a job offer letter. Stating that all I needed to do was reply in kind with a letter of acceptance. I did that as well. The next email received stated that to perform my job successfully I would need to get a printer, a licensed booking software and that they were going to send me a check for $2,950 in order to get the printer, printer paper, licensed software and to pay my first weeks weekly pay of $400. All that was asked for is my Correctly spelled name and my home address to send the check to. Is this some type of scam or do I have a legit job here?
It's a scam.
See here for just one story on the fake job, fake check scam.
The usual pattern is that the check is fake but it will take some time for your bank to detect this. In the meantime, you will be asked to do things with the money that wind up giving it to the scammers such as wire money to pay for "supplies" from dealers that are actually the scammers. When your bank detects that the check is fake or stolen, they will reverse the deposit leaving you on the hook.
You'll cash the $2950, "order" printer, software, etc at the place they tell you (which uses some unreversible payment scheme) and will never hear from them again. Instead the check will bounce if you are lucky and you are out of the $2550 you paid for the "printer".
If you are less lucky, the police will knock at your door because of your participation in a money laundering scheme. You'll be out the $2550 plus interest, damages, penalties (which may include jail time) and the costs of a legal defense.
Either way, the bank may choose to cancel your account since you likely violated your terms of contract by using it for transferring money for someone else.