Curtis posted the class act of straight keys, the J-38. It often is a somewhat collectable on ebay but can be found for a good price at hamfests. Some straight keys have what has been referred to as a "Navy knob" which is a larger disc below the main finger knob, it provides a somewhat better grip and rest for your fingers. Several QST hints detailed using a poker chip to add this feature to any key. I have used both styles and it didn't make much difference to me but you are likely to see some set up like this if you go straight key shopping.
A good source on adjusting the various forms of CW sending devices is here: http://www.morsex.com/misc/keyadj.htm#Straight
The TO style keyer does a great job of forming perfect length dots and dashes with the proper spacing between these elements when holding either the dot or dash contact closed and it does so using fully electronic circuits which was fairly revolutionary for its day but it is very different from modern electronic keyers. I hooked my TO up last night to try it out and it does what it was meant to do without issue. But it is definitely not an iambic keyer, hold the paddles together and you get nothing but dashes. Keyer paddles designed for it and similar were a single lever held either to the right or left, modern paddles will work fine but don't squeeze them. There is no dot or dash memory or any buffer so your actual keying speed has to match the TO, otherwise you will either drop or add elements.
Current keyers are iambic, have dot and dash memory, and will provide proper spacing between both dot, dashes, and in combination when used in iambic or element insert mode. Many also have automatic character spacing so that within a certain manual length of time between characters it will automatically set spacing to the correct amount. Weighting (dot to dash length ratio) is easily adjustable in modern electronic keyers. Basically, if you learn with the TO keyer you will not be learning the style used with more current electronic keyers.
I would start with a straight key and become proficient with both sending and receiving and then probably move to a modern electronic keyer while saving the TO for fun operation with a classic vintage type keyer. Note that not all modern keyers are suitable for keying older rigs because they will exceed the voltage and/or current capabilities of the keyer's keying transistor. Your HT-40 is cathode keyed which puts a fairly high open terminal voltage on the keyer. MFJ used to rate several of their keyers for cathode keying but I don't know if that is still the case. Learning how to tune up a vintage transmitter doesn't make it more difficult to use a modern transceiver but learning on a keyer with very different characteristics from its modern counterpart will make the transition difficult because sending is a fairly cognitively involved process. Some would question why not just use a computer or keyboard (or even why use Morse at all). My view is code is fun and I enjoy the interaction with the mode that you cannot get through a keyboard. My Drake TR-7A came with the matching Theta 9000 keyboard which sends and receive Morse and RTTY and another group of gear came with a Hal keyboard and monitor and both are interesting but I don't use them often. I prefer to send my Morse somewhat manually and a keyboard takes away from that experience. You might find one of these code readers or your computer/soundcard with a Morse decoding progragm to be useful while learning to send with whatever you use because if the machine cannot read your Morse then it needs more practice