The thing with Medieval Latin is that, as you figured, it’s such a vast corpus that’s hardly possible to speak about it in general terms. Some authors will write such a clear Latin that, if it weren’t for the subject matter, you would think you were reading Cicero or Livy. Others will muster such an array of vernacular words that will make it hard for you to know whether you’re reading Latin or French with something that passes for declensions.
This is Medieval Latin from John of Salsbury.
Iucundissimus cum in multis, tum in eo maxime est litterarum fructus, quod omnium interstitiorum loci et temporis exclusa modestia, amicorum sibi invicem praesentiam exhibent, et res scitu dignas situ aboleri non patiuntur. Nam et artes perierant, evanuerant iura, fidei et totius religionis officia quaeque corruerant, ipseque recti defecerat usus eloquii, nisi in remedium infirmitatibus humanae, litterarum usum mortalibus divina miseratio procurasset. Exempla maiorum, quae sunt incitamenta et fomenta virtutis, nullum omnino corrigerent aut servarent, nisi pia sollicitudo scriptorum, et triumphatrix inertiae diligentia, eadem ad posteros transmisisset.
And this is Medieval Latin as well, from an Aragonese chancellery document I was working on a while back.
Pro parte Anne converse uxoris d’en Cresques judei quondam buxolerii Majoricarum fuit coram nobis expositum querelose quod vos ad solam instanciam et requisicionem Dulcie converse uxoris Jacobi Ribes quondam inventariari fecistis seu in sequestro poni aliqua bona, raupas et aliquos libros in posse Ludovici ça-Granada conversi existentes pro securitate alimentorum per eundem Lodovicum dicte Anne prestitorum, que et qui erant supplicantis predicte, Anna prefata non anxia nec vocata, quodquidem inventarium seu sequestrum vos licet pluries requisitus revocare seu cancellare noluistis.
This remains true: for how long people were writing in Latin, whenever they could they would tend to place themselves in a tradition of vocabulary, syntax etc. If you want to read Paulus Diaconus it would be good to have read Livy first; if you want to read Einhard it would be good to have read Suetonius; if you want to read… etc. You can take it from here. There won’t be a single thread that’s called Medieval Latin, it’s as much a cliché as it is true to say there are rather many kinds of Medieval Latin, which even while held together by the prestige of Classical authors (even if that prestige must be always checked by the education of the writer and the availability of the works in question) will be constantly checked by the date (if we say ML is from 400-1400, that’s a thousand years!), by the region where the person’s writing from, etc etc.
Just enjoy yourself. Start from where you’re most interested and read from there, don’t be overly worried about whether you’re doing a “right course”. If you are so worried, start with Augustine and Boethius so you get a ground start for something that’s firmly both Classical in tradition and Medieval in outlook. If you’re feeling at a loss an amazing place to start is the Dumbarton Oaks Medieval Library (also featuring Eastern Roman == Byzantine and Anglosaxon literature).