Sorry, I don't think there is a printer and monitor calibration tool in your budget. I've used both Xrite and Datacolor and the version you need (like the Datacolor SpyderPrint) presently sells for around $350 in the US. I've used both companies and Xrite is more technical and the Datacolor wizards are easier.
What is frustrating is that CMYK of reflected dyes or pigments on paper is never going to translate the exact same as pixel light RGB from a monitor. Because we start the process with a vibrant monitor, as you calibrate the two, you'll find the CMYK reality to look much lower in contrast, saturation, and tonality. There's also going to be a difference between a 300 dpi print vs. either a standard def monitor at 72 ppi, an HD monitor at 96 ppi, or a Retina display at 220 ppi.
Is This Retina? - DPI/PPI Display Calculator
The ambient light and color in your room with the display and printer also affects our perception. I have messed and tweaked with ICC profiles and have come to the conclusion after years of experimentation that the best and most consistent results are the ICC profiles established and tested by the manufacturers. So you start with the best monitor and printer you can afford. For me that's a retina Mac and an Epson printer. Then I would get a sample pack of papers of inkjet paper stock I know I can obtain and afford. I use a color image with a high dynamic range and with more than one skin tone. I also use a black and white image that has all tonal zones from paper white to no detail shadow black.
Before you run the test, I would calibrate your monitor to either the default or to the customized one most monitors come with. On the Mac you can do that in System Preferences.
When you print on the various paper media, make sure you consistently go through the printer settings dialog boxes to select the same quality settings and for color matching, I've gotten the best results using the printer's color settings and not ColorSync. Make sure the media is selectable in the print settings (such as Epson Premium Photo Luster), and if not, download and install that first. Of course for monochromatic images, make sure you've selected black ink only or 'Advanced B&W'.
I did this with over 20 different papers, some cheap, some expensive, different surfaces, manufacturers, different grades of quality. The evaluation will differ depending on the judge and your subjective aesthetic response. For me, the Epson papers outperformed all others including some very expensive non-Epson papers, even though I had their profiles in my print settings dialog box. A lot of my final decision and more to do with how the ink had dried or was absorbed onto the paper in 24 hours. Big difference between coated and non-coated papers. No doubt if I had a Canon printer, Canon paper would have performed better. But there are also tons of specialty papers and again it all comes down to your personal preference, price, availability, printer ink compatibility, and print drivers.
One other piece of the puzzle is Color Space/Color Mode. The default on cameras is sRGB which looks great on a RGB monitor. But I change mine to AdobeRGB because I am going to use Adobe BR, PS, or LR to process my image with the final intent of printing. If I had even better equipment, I would convert everything to ProPhotoRGB for better bit depth.
For me, this process works better than using custom created ICC profiles. I am involved with a book publisher, and although we send our images with ICC profiles (to either a digital printer or offset press), I still have to fly 4,000 miles (one way) to physically inspect during a press check for color as well as black and white density and contrast before we go to press. Sorry for the long response, but if you're still reading, a color calibration tool is not cheap and is not a magic wand. Every step of the process from camera settings to software/drivers/print settings to the printer and media, as well as the ambient color temperature and light level is throwing a curve in achieving your goal.
Back in the day, the photographer had a favorite emulsion/film, a favorite lab, and bonded with that combination. Many photographers still go that route with everything from Costco to Shutterfly to some custom labs like the FINDlab or A&I.