First off, I'm a ham, originally licensed in 1979, so not yet an old timer. Most of my operating time in the last fifteen years has been VHF/UHF/microwave. I've owned lots of "normal" HF radios, and a few VHF and UHF radios. (Coolest was a Signal/One CX-7A, sorry I ever sold it.) I also spend a lot of time with a modern SDR.
SDR is a whole lot of fun. But it is very hard, and perhaps impossible, to find an affordable starter's SDR based HF radio. VHF/UHF is probably a different story. (I have an Ettus N200/UBX on my desk here. It tunes from 10MHz to 6GHz. It is <not> a starter's radio.)
Well designed HF radios carefully apportion gain in the RX chain between the antenna and your ears to ensure good performance in the presences of very very strong interfering signals. Imagine trying to hear a 100mW signal from 300 miles away while your radio is being blasted by a 50000 W transmitter just 30 miles away.* That's a 60dB difference in signal level BEFORE we account for the path loss. In the ideal free-space world, the actual difference would be something like 80dB. Yes there are tricks in SDRs to improve the dynamic range, but it costs money to get to that point. If you want a radio that can deal with the very very noisy HF environment, your best bet is to go analog.
Yes there are SDR HF transceivers with good IMD performance. But they are very expensive. I can't imagine that spending more than $4000US for your first HF radio is a good idea.
VHF radios are a different story. There are still intermod issues and dynamic range considerations, but they are much easier to treat (in my experience.) An SDR receiver for VHF/UHF could provide some interesting opportunities even in the beginner price range.
But if you want to get your feet wet on HF, find an "analog" or at least not-so-SDR rig. I have an FT817 (HF,VHF/UHF) that is just fine. Yes there are better. (especially since the FT817 makes some compromises in that balance between front-end-gain and dynamic range) There are also radios that are much cheaper and a joy to operate. I've owned a few TenTec transceivers that were simple, fun, easy to work on, and performed well. No doubt other posters will have suggestions of their own. Find a local ham who can help guide you, and don't spend a lot of money on that first rig.
I won't be surprised if someone posts that they've been operating on HF with an SDR built out of two TTL inverters and a length of coat-hanger wire. Good for them. But I have and use a moderately expensive SDR with software that I've been developing for a long time. I have an FT817 right next to it. The 817's performance is head-and-shoulders above the SDR on frequencies below 20 MHz or so. Above 50 MHz the SDR wins, hands down. In time, I'll add front-end filtering to the SDR. It will improve things a bit, but there are lots of intermod sources that will still be in the passband. (Note that most of the off-the-shelf inexpensive SDR's have very broad front-ends -- some have no filtering at all, others have filtering that isn't so good.)
All that said, the RTLSDR is loads of fun. There are interesting signals to be found in the VHF spectrum. Yes, it can get crunched by strong signals. But for $20, it makes a good platform to learn a little about SDR and play with some neat tools.
And if, after all this, you do go with an SDR for HF, find one that is designed for HF. Radios that tune from "DC to Daylight" mix products from "DC to Daylight" and create lots of signals that aren't really there. They really need front-end filtering to be adequate.
*The illustration is based on an AM broadcast station (well out of band) vs. the desired signal in an HF ham band. Say an AM broadcaster at 1300 kHz and your desired signal at 3.9MHz. There are no "perfect" filters, and that AM signal is going to look pretty tasty to the first semiconductor junction it sees.