It is a tight budget but not impossible. If you want to get best sound quality consider buying one item new and one item used. IMHO a new budget amp with used bookshelf speakers. Even at entry level speakers don't suffer much from use, but electronics does deteriorate. So get a new integrated in 25-30 K and a used speaker in 10-15 K.
While am unfortunately no longer well versed at this price point, don't rule out a Chinese integrated amp, they can offer good value for the price. Otherwise the Denons' and Marantz's are there which are also made in china. Not sure if Lyrita makes anything in this range anymore, but there are other Indian DIY builders you could find out about.