There's no right way to start your art portfolio necessarily. That's unless you're looking at your portfolio in the terms of an investment. If you're looking to start an art investment portfolio then you must take into account what you're purchasing. What I mean is, you can't just go purchase art from IKEA or from a small relatively unknown artist. Because the likeness of this artwork increasing in price and you being able to resell it for more in the future is slim to none.
You need to purchase artwork form an established artist, one that has a career underway and is growing. If you'd like some recommendations, I've made a list of 5 Contemporary Artists who're not just affordable but gradually growing in their respective art category. Keep in mind art has forms and each one is very different. From toys/sculptures, furniture, prints, paintings and more. Then there's art movements, such as contemporary, pop art, street art, abstract and more.
My personal preference are prints, I go into why extensively here.

Between the Sun & Moon - Cleon Peterson
So you do need to first explore what type of art grabs your attention. I've listened to countless podcasts/interviews, read books and more on investing. The first piece of advice everyone always mentions, is you must like what you're investing in. This applies to any type of investment. Make sure you like the art you're purchasing, even if it's an investment and you're looking to sell it in the near or distant future.
The best piece of advice I can give someone looking to start their art portfolio is .. START!
What do I mean? Go find an artist who's work is accessible and buy your first piece. When you purchase your first piece, you get involved in the artist because you now own artwork from them. Slowly you'll find yourself researching similar artists to the one you purchased. You gradually start eyeing out pricing for this artist's work on sites selling their art. Auction houses, galleries or private collectors websites.

Everything starts with your FIRST purchase/investment. This goes for any type of investing being stocks, precious metals, crypto .. anything. You must start a position in order to be able to say you're invested. Learn as you go about the space, visit museums/galleries, follow artists on instagram, watch documentaries. This is how you will learn in depth about the space.
6 STEP BY STEP GUIDE - Summarized
1 - Find out which TYPE of art is appealing to you (forms/categories listed above)
2 - Decide on a budget, how much you'd like to spend on your first piece
3 - Research various artists and find out not only one you like, but an established artist
4 - Now that it's time to buy, decide whether you're purchasing newly released art or perhaps you're purchasing from a gallery, auction house, etc.
5 - Finally, you own your first piece of art in your new art investing portfolio. Now it's time to stay updated with this artist, track the artists latest sales at online galleries, artsy, private sellers and more.
6 - Acquire more art, learn about other new artist and keep track of your art portfolio value.
If you have further questions join our community on Reddit / Investing Art