Bienvenido a Plovdiv Sr, @Julio Manu!
Like @PlovdivEd, we also live in Plovdiv, and he's right that it's a great place to live. Most of the city is very nice, so it's unlikely you'll pick a bad area (and there usually aren't many rental offers there). If you have the budget, or you're planning to work in the city, then in or near the centre would be good.
These days, many of the cheaper offers are in the outskirts of the city. Not bad areas, but further away, so you have to think about transport/commuting. But it's a pretty small city, objectively, so city limit to centre (5km maybe) is not a massive drama like London, for example. Indeed, many folks live just outside the city and find it a manageable distance (e.g. Markovo village is very popular at around 10km).
Personally, I like a bit of outdoors and being close to the parks. The river Maritsa runs through the city, so it's nice to be near this (Karshiaka and Marasha I think. north and south sides, respectively). There are also several hills (it's the City of the Seven Hills). They're not high, of course, but two in particular (Alyosha/Bunardzhik and Youth Hill) have very nice parks and winding cobbled paths to the top.
We chose Hristo Smirnenski, to the west, and I highly recommend this area. Lots of local facilities, but still very close to the centre (about 2km) with easy access by bus (1 lv), taxi, personal car... or use your bike/legs/escooter on the new walk/bike network (10 minutes on my escooter, very easy). Within a few minutes walk, I can get to the Regatta (international rowing) lake and Maritsa river (with the woods), Alyosha, and Youth Hill.
I suggest the websites Alo (dot bg), Imot (dot bg), and BulgarianProperties (dot com). The last is very expat-friendly, and you can easily do a rental deal remotely, if you want to have a long-term place arranged before you arrive. Otherwise, Airbnb/Booking have plenty of short-term options. As others have suggested, the most convenient option is to rent short term first, and use that to look around the city and view properties at your leisure. The downside is that it can be expensive (one month might = 3 or 4 months LT) ... and it's of no use if you're doing immigration processes before moving (when you typically need a proof of address such as a property deed or LT rental contract).
This site is good for general info about Plovdiv.