The IRS considers the postmark date to be the date of filing, so it's perfectly fine so long as your envelope makes it to your post office by the close of business on the due date. This is true for the return itself and any payments made by check.
If you're particularly concerned about having proof of timely filing, consider using Certified Mail. The post office postmarks the envelope in front of you and also hands you a postmarked receipt as proof of mailing. This also gives you a tracking number that allows you to verify delivery.
The legal authority for the timely filing rule is codified under 26 C.F.R. § 301.7502-1, Timely mailing of documents and payments treated as timely filing and paying.
A document or payment is deemed to be filed or paid on the date of the postmark stamped on the envelope or other appropriate wrapper (envelope) in which the document or payment was mailed. Thus, if the envelope that contains the document or payment has a timely postmark, the document or payment is considered timely filed or paid even if it is received after the last date, or the last day of the period, prescribed for filing the document or making the payment.
For international filers, also relevant is Revenue Ruling 2002-23, 2002-18 IRB 811 which holds that official postmarks from foreign postal services are also valid for the purposes of determining timely filing.
In addition to the USPS and foreign postal services, the IRS maintains a list of designated private delivery services which qualify to meet the timely filing rule. As of 2020, that list is certain services from DHL, UPS, and FedEx.
Finally, there are a number of 100% free e-filing options available if you meet the qualifications, but they are hard to find thanks to dark patterns employed by the tax prep industry.
This list allows you to cut though to the actually free programs. (There's also Credit Karma Tax, which is free and available to everyone.)
Online programs generally ask you a series of basic questions to determine what kind of income you had, taxes you've already paid, and credits and deductions you're eligible for. If you don't know the answers to those questions, it's likely that you aren't able to fill out the 1040 correctly yourself.
You should learn the answers to those questions before you file to ensure that your return is accurate. You may be missing out on money due to you otherwise.
Also note that generally, once you complete online tax programs, they will allow you to download the completed 1040 (and other forms) as a PDF before you file. You could do this to compare with the version you've already completed, and then e-file if it looks good. (And really, you should download and save this PDF for your records anyway.)
If you need more time to understand the questions or seek advice, the IRS will grant an automatic 6-month extension to the return due date so long as you file Form 4868 before the due date.