QUOTE: “high quality content is something I’d focus on. I see lots and lots of SEO blogs talking about user experience, which I think is a great thing to focus on as well. Because that essentially kind of focuses on what we are trying to look at as well. We want to rank content that is useful for (Google users) and if your content is really useful for them, then we want to rank it.” John Mueller, Google 2015
QUOTE: “Anytime you do a bigger change on your website if you redirect a lot of URLs or if you go from one domain to another or if you change your site’s structure then all of that does take time for things to settle down so we can follow that pretty quickly we can definitely forward the signals there but that doesn’t mean that’ll happen from one day to next” John Mueller, Google 2016
Note that Google is pretty good these days at removing any special characters you have in your page title – and I would be wary of trying to make your title or Meta Description STAND OUT using special characters. That is not what Google wants, evidently, and they do give you a further chance to make your search snippet stand out with RICH SNIPPETS and SCHEMA mark-up.
While Google is on record as stating these quality raters do not directly influence where you rank (without more senior analysts making a call on the quality of your website, I presume?) – there are some things in this document, mostly of a user experience nature (UX) that all search engine optimisers and Webmasters of any kind should note going forward.
A good amount of marketing on the internet can be done for free, but sometimes it's worth spending some money on effective and professional looking options. For example, although you can get free web hosting, it's not recommended. Ideally, you should pay for web hosting to make sure that your website doesn't experience downtime, as well as a professional domain name. Fortunately, you can buy both for less than $100 a year.
Ask for a technical and search audit for your site to learn what they think needs to be done, why, and what the expected outcome should be. You'll probably have to pay for this. You will probably have to give them read-only access to your site on Search Console. (At this stage, don't grant them write access.) Your prospective SEO should be able to give you realistic estimates of improvement, and an estimate of the work involved. If they guarantee you that their changes will give you first place in search results, find someone else.