Do you Need to Modify Your Wordpress Theme Files?

Well, I was using Joomla and a dedicated fan for news sites.
After migration hassles - I ported to WPress and use both Free and Paid themes.
The SEO was strangely better, sites indexed immediately compared to slow Joomla takeups. Each site I build I customise slightly for the need with either a child theme or simple stuff. I am running news and have started a commerce site - all handle traffic well. That said - some of the biggest global sites are based on WPress (with custom themes). Use eonly the plugins you need, too many slow WP down a bit.
There are lots of good guides on balance of SEO and speed for WP, google it.
In my opinion, you are good to go. Choose a theme that suites your needs, do a test installation. Spend the weekend researching. There are some freemium themes that are very customisable. That said sometimes its worth $50 to get the feel you want.

Just a side note - generally there is no problem with a free theme technically. The limitations are usually how customisable it is, how responsive and what functions (widgets etc) are included. Normally the coding is Ok. A well coded WP theme based on a clean framework will handle heaps of traffic. There is a lot of choice, and if its well behaved will play nicely with most plugins. Remember a plugin is effictively a piece of code that always runs and ads to the overhead of the site so try to keep from adding to many other than your standard needs for SEO, Membership etc

Long term issues with free themes are updates, unless you are a coder yourself, if one day theme creator decide to stop updating the theme, you will wuickly find yourself into truble as Wordpress changes very often and some codes becomes obsolete from day to another.

free themes have no tech problems at all, the problem comes when the developer stop updating it for new WP versions, if it get deprecated there is no other choice than replacing it

better get a free theme from a well know designer that keep it updated

Really just depends on your personal preference. If you have the skill to modify it your own, then go ahead. It's nice to have some uniqueness on your design and adding your personal touch to it.

Yes it sure is. You can basically do anything without a wordpress theme if you require the skill. Free wordpress themes also but they sometimes need extra customizing or have certain parts of the theme not available to you.