SiteGround added a support for PHP 7.3
Now SiteGround added the support for PHP 7.3. SG users can choose PHP 7.3 as well as other PHP version starting from PHP 5.5. You can change the PHP version for the root directory or the first level subdirectories under cPnel > 1H Software > PHP Version Manager.
Currently, most web applications, including WordPress, don’t work on PHP 7.3 yet. According to the official WordPress 5.0 Schedule Post, full PHP 7.3 support will be added in the major 5.0 update (or in the minor 4.9.9 update if it's released.)
According to PHP 7.3 Preparation Tasks, the official version of PHP 7.3 will be released on December 6, 2018.
PHP 5 will no longer be supported with security fixes, starting on 1 January 2019. So, even if a vulnerability is discovered, it won’t be fixed. PHP version 7 has many improvements over PHP version 5.
I think SiteGround is reliable and fast. If you are a quality webhosting service wigh good performances, SG will be an option. If you are looking for a cost-effective webhosting service, You might consider the Bluehost's Shared Plan.
For your reference, if you sign up for a webhosting service by clicking the referral links on this post, I will get some commission. However, I do not suggest specific services just for commission. I’ve been managing websites using several different webhosting services including SiteGround and Bluehost for years.
If you want a cheap but a good performance webhosting service, you may consider Bluehost. If you sign up for BH's Shared Hosting by clicking this link, you will be able to purchase Bluehost webhosting service with US$1/mo off.