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As always, there will be people who will try to convince you you must have the latest wiz-bang commercial interface, and indeed many people are satisfied with those.
While I have nothing against such interfaces, you need to know that it is not necessary to shell out $80 or $100 or more to find out if you are interested in digital modes.
I recommend you try out a simpler method first, and if you like it and want a more "professional" solution then you can spend your hard earned cash.
Depending on your rig and your setup, the solution can be as simple as a stereo cable with maybe an RCA-mini jack adapter (to get to the computer's sound card input and output). This assumes the rig can be made to transmit via the serial port (see below).
I use this solution quite satisfactorily. I have made a number of RTTY QSOs using MMTTY. My laptop is not powerful enough to run the digital modes under Logger32, as it only has a Pentium 120 MHz, but it runs MMTTY very well and WinPSKse (for PSK31).
I have used the cable with both my TS-440S/AT and my FT-1000MP Mk5 Field. Both radios have RCA jacks on the output. I have used the same solution with my FT-817, even though the cable is more complex (the radio does not have RCA jacks, just a mini-DIN connector, which is harder to find, see link to All Electronics below).
If your rig cannot be made to transmit via the serial port, or if you do not have and do not wish to interface with the serial port, it gets more complex (!) as you will need an additional cable with a NPN transistor and a 10k resistor to key the rig from either a serial or parallel (printer) port. That will involve some soldering for sure :-)
You can look at my ham radio page for my various interfaces.
The only problem I ever had was RF feedback, which I did experience on some bands when the 7 elements beam was pointed directly at my upstair shack. This was cured by a couple of ferrite beads rescued from old computer monitor cables at each end of the audio cable. You can also buy inexpensive ferrite beads of all shapes and lengths from All Electronics (I have no affiliation whatsoever with All Electronics, I am just a satisfied customer).
Some people will also tell you you must have isolation transformers to prevent RF feedback. This is rarely true as the audio transformers typically have so much capacitance that the RF path will be hardly affected by the transformers. Please note that an improper installation of a commercial interface will also create opportunities for RF feedback. Commercial interfaces are NOT a necessary solution to RF feedback problems.
However, transformers can be helpful if you have hum. Hum is typically due to ground loops between the computer and radio causing 50 or 60Hz (your line frequency) to appear on the audio lines and if you have hum, transformers are an easy and effective way (but not the only way or even the best way) to eliminate it. In most cases, a solid ground braid between computer and radio will take care of it and be a better solution than transformers anyhow.
Bottom line: it is quite simple and absolutely does not have to be expensive to add digital modes to your arsenal. The commercial interfaces only make it more complicated because instead of a single cable between the radio and computer (and maybe a ground braid), you now need cables to and from the commercial interface, and the supply cable for the commercial interface. In my opinion, this is a "solution" looking for a problem.